system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5:What are the main beliefs of major Christian Denominations? (Methodism, Baptism, Catholicism, Anglicanism, LDS etc.)
gpt
This is not a topic that lends itself to ELI5... at all. And most of the answers here are not helpful, and many are outright wrong on one more major branches.

Historically Christianity has never been in total agreement about its own beliefs. And that is nothing unusual. Most religions have a lot of variants in beliefs. But for the first several centuries Christianity was attacked from outside by Greek and Roman pagans who saw Christianity as something new and dangerous. And it was "attacked" from within. There was always disagreement about what Christianity meant. Eventually a certain group won out. This became the "Orthodox" (Greek for "right belief") and "Catholic" (Greek for "universal") church. It was run by bishops, the most important of which were the Patriarchs, the most important of which was the bishop, or patriarch of Rome (also called the Pope). And their rulings were enforced by the Roman Emperor.

However even then not all Christians fell into this same belief system. There were Nestorian Christians to the far East, various Oriental Orthodox churches in the Middle East, and the Ethiopian church in Africa. But for the most part they tended to follow the same sorts of beliefs. The one big exception would be the Arian Christians to the North. These were mostly Germans. And their big disagreement was on the nature of Christ. For them Christ was a created being and lesser than the Father. This was heresy to the Catholic Orthodox Roman believers.

Now we skip forward a number of centuries to the great schism. In the west by this point you had a bunch of European (mostly German) kingdoms. And in the east you still had a Roman (in name Greek in language and culture) empire. And the Pope and the Emperor didn't agree. So they split. On points of doctrine they are very close. But the eastern Orthodox churches don't accept the Pope as the boss of all bishops. Instead they see him as the most prestigious, but with no more authority. So the Orthodox churches (Greek Orthodox, Russian Orthodox, etc) all have a Patriarch as a head bishop and are mostly the same. And they are all very similar to the Roman Catholics who look to the Pope as their Patriarch.

Fast forward a few more centuries and we come to Martin Luther. In the West the church always had an odd role, it was at an arms length from the government. In the East they were always either completely in control of the government like in the Byzantine Empire, or completely out, like in the Ottoman Empire. But in the West. The government and church were separate. But intertwined. And sometimes they completely reintegrated and you would end up with a Bishop with estates like a regular noble. But even when that didn't happen, the church was frequently responsible for government style functions. And so they regularly needed to raise cash. Taxes were and option and the Catholic could and did both tithe and tax people. But they also occasionally could get creative thinkers. And one of them came up with the idea of selling indulgences. Basically (and this is a gross oversimplification) they were a get out of purgatory card. They were forgiveness for sins not yet committed. And Martin Luther found them (and a lot of other things) objectionable). So he protested. And a bunch of other people went along with it. This became the third major split point, Protestantism. And a lot of the early branches (Lutheranism, Anglicanism) are still very similar to Catholicism. Basically they can be seen as minor reforms of Catholicism. But Luther introduced a fascinating idea. Prior to him the Bible was seen as only equal to tradition. And the Bible had to be interpreted through study and knowledge of that tradition. Luther put the Bible above tradition and said that all believers were entitled to both interpret it and to receive inspiration from God. And that is where things take off. For the most part most Protestants are in Communion with one another. So a person can change churches without major difficulty. And even religious leaders (pastors) can change without too much fuss. As long as a church accepts the early Christian creeds like the Nicean Creed, it is all pretty much just a question of preference to most modern Protestants. 

The last big movement in Christianity started in the 19th century. That is the Restorationists. This is an attempt to return to basic Christianity striped of all other trappings. Of course few Restorationists seem to be able to agree what really consists of a core part of Christianity and what is a trapping.

Ok on to specifics.

Catholics - In the West this is the default that the "early" church evolved into. They believe the standard Bible stories (actually they include more in the bible than most Protestant churches). They have Popes, Cardinals, Bishops, and Priests. The revere (not worship) saints and Mary. And they have Tradition, with that capital T, and pomp and circumstance.

Eastern Orthodox - Mostly you can think of these as Catholics without the Pope. They tend to form on national lines, with a Patriarch acting as the head of the church.

Oriental Orthodox - Much the same thing. These guys split even earlier. These include the Copts in Egypt, the Armenian church, the Ethiopian church, and such.

Lutherans and Anglicans (Episcopalians) - These are basically Catholic without the Pope. Early reforms stuck and after that no much else was changed.

Baptists - An amalgam of a lot of other ideas, so much so it is hard to talk of a Baptist doctrine. But they don't believe in a hierarchy. Baptism is not "necessary" to be saved, but if it is to be done it shouldn't be done to infants, and should be done by complete immersion.

Methodism - Anglican in origin with a focus on the "poor" and a "methodical" approach to spirituality. Basically a simple, straight forward, middle class American, Episcopalian.

Presbyterian - The Scottish church. When the English church split from the Catholics it kept bishops and cathedrals. The Scots took it a step further and only kept the priests (Presbyters) and local churches. A root level Anglicanism.

Pentecostalism - This is a Restorationist church. They believe in and focus on the gifts of the spirt that were poured out on believers on the day of Pentecost. So they believe in speaking in tongues etc.

Adventists - Another Restorationist church. The focus is on returning to Saturday as the traditional day of worship.

Jehovah's Witnesses - Again Restorationist. They believe only 144,000 will actually live with God (in Heaven). The rest of the worthy will be resurrected to Earth like it was in the Garden of Eden times. Jesus is NOT God of any sort.

Mormons / LDS - Restorationist, but of a different flavor. They believe in Prophets of the Old Testament flavor. Joseph Smith was one of them and literally spoke to God, Jesus, Peter, James, John, and a host of other Biblical and Angelic beings. He is supposed to have translated multiple new books of scripture and added more new revelations on top of it. In a lot of ways the LDS are something new rather than just another denomination. They believe in the Bible. But they believe in so much more. Unlike the other Restorationists, they aren't trying to piece together the primitive church from what the New Testament says, they putting together a new church according to what God wants now, which in some ways resembles the early church.