What's the difference between religion and mythology? The technical answer is probably something along the lines of "religion is a belief in a real and existent deity, while mythology is the belief in non-existent supernatural beings." But the more accurate answer is religion is what the guys in charge believe and mythology is what the guys who used to be in charge believed.
The ancient Greeks are famous for their mythology that focuses on the Gods of Olympus and their impact and influence on humanity. However, when the Roman civilization expanded into Greece, the Greek Gods were co-opted by the Romans, renamed and new stories were told about them. The Roman Gods became the new religion and the Greek Gods - despite essentially being the same characters - were relegated to fictional status. Likewise, when the crusaders came, the Roman Gods were replaced with the Christian God and once again, the old religion became the new mythology.
So what made the ancient Greek's supernatural explanations for the unexplained any different from the modern Christian ones?
The ancient Greeks - like any civilized society - were fascinated by the unexplained. The quest to understand the world around them led them to create "Gods" that were responsible for those things in nature that couldn't easily be explained or credited to man. So, when the question is asked "where does rain come from?" or "Why does the sun rise and set and move across the sky?" or "Why is it hot in the summer and cold in the winter?" the answers to all of those questions was "There's a God for that."
Of course, there also had to be a God-based answer for why things didn't go the way they were supposed to. "Why is there no rain?" "Because the God who provides rain is angry!"
This belief system served the ancient Greeks well. Things that they couldn't explain were suddenly explained and the vast wisdom and knowledge of the Greek people was intact. And, really, isn't that what religion is all about? Creating an answer to the questions that you don't know the answers to so that you don't have to admit that you don't know everything?
When the ancient Greeks found themselves unable to explain rainfall, they created Zeus, the God of thunder. When the Greeks were unable to explain death, they created Hades, the underworld and purgatory. When they were unable to explain love, war, the sun or the unpredictability of nature and the hunt, they created Gods for all of those things as well. As the Greeks discovered science, their society developed another fundamental religious practice - the stretch of logic.
As I mentioned before, the Greeks believed that Zeus brought the life-giving rain to the fields, but when there was no rain, rather than assume that it was because perhaps a God didn't control the rains after all, they surmised that it was instead because Zeus was angry with the people. Thus, whenever the natural course of unexplained events in the world went in favor of the people, it was because the Gods were happy and were conducting their business as usual, but whenever things didn't go as planned, it was because the Gods were simply angry. Why was there summer 6 months out of the year? Because Demeter, the Goddess of fertility and the harvest, was happy and brought the good weather. However, when it was winter for 6 months out of the year, it was because Demeter was sad and refusing to bestow her bounty on the people. Why was Demeter sad? Enter the story of Persephone and Hades.
But, strip away the use of the Greek Gods to explain those things that were unknown at the time to the ancient Greeks and what do you have? You have a very familiar story.
The ancient Greeks believed that, originally, the world was ruled by the titans and their leader was Cronos. Eventually, Cronos' son, Zeus, would rise up with his siblings and an army of cyclopses and overthrow Cronos to take control of the heavens and become the new king of the Gods. The titans were banished to Tartarus (purgatory) and the new Gods were now in charge of everything. The theme of the rebellious son rising up against his father to try and usurp control of heaven is a central theme to nearly every major religion, including Christianity.
The biggest difference between Zeus' coup against Cronos and Lucifer's mutiny against God is that Zeus was successful and became the new king of the Gods, while Lucifer failed in his overthrow attempt and was cast into purgatory (Tartarus?) Thus, Zeus enjoyed the victory that became God's victory to the Christians, while Lucifer endured the defeat and banishment that was Cronos' punishment in ancient Greek mythology.
Perhaps it's the introduction and wide, societal acceptance of science that added a legitimacy to modern religion that was easier to dismiss with ancient mythology?
Greek Gods were created to explain those things in the lives of the ancient Greeks that were unexplainable at the time. The pervasion of science and the dilution of the Greek beliefs through conquest and intellectual evolution weakened the belief in the Greek Gods, who were replaced with new Gods that were tailored to explain their way around the new, enlightened society.
Thus, the more science explained the tangible aspects of nature that had previously been credited to the Gods; the role of the modern, Christian God became less of a hands-on approach and more supervisory. So, while the ancient Greeks believed that the sun travelled across the sky as a fiery chariot, driven by Apollo, the Christians - who discovered that the sun was a ball of fire and exploding gasses in space - accepted that there was a logical, scientific explanation for what that ball of sun was and instead gave God credit for creating the sun in the first place.
The theory of creation is the foundation of the ability for Christians, living in a post-scientific world, to continue to give a supernatural God credit for the naturally-occuring and scientifically-explainable objects and events in the world around us.
We know that the oceans are controlled by gravity, weather and the moon, rather than Poseidon, so Christians give credit to God for making the ocean, making the weather, making the moon and allowing gravity to exist.
We know that good and bad weather is a product of a random series of forces, from atmospheric conditions to even cosmic factors and the rotation and revolution of the Earth, but Christians give credit to God for making the Earth, for placing it on it's path through space and, yes, they still pray to their God for rain during a draught or sun during a monsoon.
Is there much difference between the ancient Greeks (and Christians too), who believed in giving burnt offerings to the Gods for a good harvest and modern Christians, who believe in paying tithes to the church to thank God for their blessings and persuade him to continue to send more their way?
Christians streamlined Greek mythology. They reduced it from 12 Gods and Goddesses to one omnipotent creator. They kept the "son vs. father" aspect of the story, but made God the victor instead of his insubordinate son. They adapted the story to fit with the evolution of logic and society, so that instead of God running around doing everything himself - which could be easily disproven - he instead now chooses to sit on his heavenly throne and watch mankind navigate through the world he "created" for us, like an ant farm or aquarium full of fish.
However, there is just as much evidence to prove the existence of God as there is to prove the existence of Zeus.
The bible is the story of God, just as the ancient epic-poems and carvings were the story of the Greek Gods. Church hymns praise God, just as ancient Greek ballads praised their Gods. Christian artists have created numerous renderings of God, Jesus, angels and demons, as ancient Greek artists painted the Gods, monsters and demigods of ancient Greece. Yet nowhere in either culture is there a significant historical account of the physical existence of either the Greek Gods or the modern Christian God.
There is no historical account from ancient Greece that speaks of a God walking the Earth, impregnating women and birthing demigods, as Zeus and the other Gods were credited with doing in the mythology. There is no archeological evidence of the existence of minotaurs, cyclopses, winged horses, gargantuan sea beasts or the like. The only records of these people and events are in the stories of the mythology, the teachings of the "religion" of the day.
Likewise, there is no historical account of the existence of Jesus as Christians know him outside of the bible. There is no evidence of things like Noah's Ark or the remains of Sodom and Gomorrah. Of course, if you ask any Christian, they can easily explain that. I mean, of course there's no evidence of Sodom and Gomorrah, God wiped them completely off the Earth. Of course there's no remains of Noah's Ark, God saw to that as well. Of course there's no historical mention of Jesus outside the bible, and it's either because Satan influenced people not to write about Jesus or there's the other common Christian explanation "Of course there's historical accounts of Jesus outside the bible, there is TONS of evidence of his existence!" Of course, most of that "evidence" is simply just more stories written by Christian theologians, not any actual historical documentation, but that gets us back to the human arrogance that led to the creation of the concept of Gods in the first place.
Throughout history, Gods have existed as a means of explaining those things which mankind could not explain at the time. As mankind discovers the true, scientific reasons for those unexplained things and events, God continues to exist as a means of explaining that which we still haven't figured out as well as assuming a historically "newer" role of being more of a benevolent observer - a role that allows God to retain his omnipotence and power without having to actually do anything to prove his existence to the non-believers.
It all stems from simple arrogance, though. Man doesn't want to admit he might not have all the answers, so he creates a God to solve for "X". Later, as man begins to find the answers, he modifies the role of God from the cause of all of those things to the overseer of our existence in his world. God has evolved from creating the rain and causing wars to creating the Earth upon which rain falls and wars are fought. The only constant is the refusal of religious society to admit that there are just things we don't yet understand and that mortality is still the greatest, and scariest of those unexplained mysteries.
We created heaven because the sentient mind of man couldn't handle the notion that there might not be anything waiting for us when we die, that death could just mean dying and no longer existing in any form, anywhere, anymore. Religious society can not accept that we aren't destined for something far greater than our finite, mortal lives. Arrogance and fear, the belief that human beings are far too special and important to simply die like everything else on the planet and the fear that this might actually be the case leads intelligent, educated and rational people to believe in an invisible, all-powerful deity who directly or indirectly controls every aspect of every minute of every person's life on this planet, while also controlling the planet itself and everything in the known universe. When things are going good for you, it's because God wills it. When things are going bad for you, it's also God's will. When the rain falls, God wills it. When there is draught, God willed it. When the flood waters rise, it's part of God's plan. When the earth quakes, it is God's will. When good people die, it is part of God's mysterious plan. When bad people succeed, this too is God's plan. When you are fortunate in life, it is God's "blessing" upon you, and when you are cursed with bad luck, it is God "testing" your faith.
As the mind of man has evolved to understand that which used to be a mystery, that same mind has also evolved God's role in religion to that of a circular argument to which there is never a truly effective argument in the mind of the faithful believer. For every question, God is the answer, no matter how contradictory that answer is. "Why do we feel good?" "Because God is rewarding your faith!" "Why do we feel bad?" "Because God is testing your faith!"
"Why do we worship one Christian God instead of 12 Greek ones?"
"Because the Greek Gods aren't real, silly!"