I know about "protestant", "catholic" and then there's something else in the "main three" which I probably "should know" by heart but I simply don't.
(Probably referring to Eastern Orthodox?)
And then there's also things like Mormons ("Latter Day Saints") and many other minor "variants".
Yup. Add to that, Jehovah's Witnesses, Seventh Day Adventists, and others. (I singled out those two because, like Mormons, they use writings that may be generally accepted by fewer of other mainline Protestant branches.)
It would be much simpler if there were just "Christians", "Muslims", "Jews", etc., but it's apparently not enough to be "Christian", because all the different groups of Christians will not approve of you unless you use their "variant".
This is not Christian-specific. Muslims have the Sunni (the larger group) and Shiite/Shia.
The Christian sacred texts (books from the "New Testament") contain multiple references to Jewish sects, probably most notably the Pharisees followed by the Sadducees, but there are others like Zealots. There were also Samaritans and Hellenists.
Within the Protestant branch, you have a group called "Christian Reformed". Some people there may be a "five point Calvinist" (using a term named after a famed theologian named Calvin), but others might just be a "four point Calvinist" because they don't accept all five points of the traditional 5 point Calvinists.
I mean, why would they exist if they all agreed to the same stuff anyway?
Right. Mostly. Umm... Err...
The truth is that many churches tend to want to have a denomination as part of their name. However, in many cases, the selected denomination ends up being little more than just a part of a name, especially after time and after a change like a new pastor. You end up having Baptist churches that are more Lutheran than they are Baptist, and you have Lutheran churches that are more Baptist than they are Lutheran.
How true that is can vary. For instance, the Seventh-Day Adventist church has a pretty centralized hierarchy, similar in structure to the Holy Roman Catholic church (the church you probably know of as the "Catholic" church). But even then, there can be branches like members of a Branch Davidian group that banded together in a famous fatal stand-off in Waco, TX.
Even within the churches, you will then have some people who are more serious about religion than other people, and among the people who are more serious about religion as a whole, you will find that some people place more importance on some teachings than others.
So, yes, it is true that the the Presbyterians and the Methodists may have some difference. But that doesn't mean that there is a ton of agreement even within a single denomination.
As an example: I remember going to Cornwall Church of God, and in a class for people interested in becoming official members of the church, people were being told that they are technically part of the "Church of God" denomination, but it was just a technicality. Years later, that church officially stopped being part of that denomination altogether.
That particular (rather large) church ended up becoming officially "non-denominational". Several churches have embraced that term for themselves, or "evangelical" (which basically means they evangelize, meaning they spread their beliefs. There is essentially no difference at all between "evangelical" or "non-denominational". But, for that matter, some of the other established denominations have been losing their distinctiveness too.
Some (a lot, in fact) even say that Jesus was a Jew
The first seventeen verses of the New Testament start with "The book of the genealogy of Jesus Christ, the son of David, the son of Abraham." That Jesus was a Jew is just not an item in wide dispute. If someone wished to contest such an established fact, then one would wonder how many other established facts would be similarly disputed. For instance, if they are so quick to toss out such uncontroversial text in the bible, what remaining parts of the bible would they embrace? There are usually much bigger opportunities for disagreement than that one.
So, yes, Christianity grew from Judaism. When many members of Judaism did not embrace the changes in religious understanding that were surrounding Jesus, then those who embraced Jesus became known as Christian. The others became known as "Orthodox Jews", although are often just called "Jews". From the Christian perspective, they follow God and so did the Jewish nation before the time from when Jesus was born, and Christianity is simply the correct continuation of the God-following people who were previously known as "Jews". But when the Orthodox Jews resisted the new understandings being taught by the Christians, the Christians happily accepted their new name because they didn't want to shy away from the name of Jesus Christ.
In fact, I have never heard of any Christians who refer to the "protestant Bible" or "catholic Bible" -- it's always just "the Bible" (by which they mean the old and the new testaments combined, I assume)
Actually, these definitely exist. In short: The Jews have their main scripture which contains the same books as the protestant's "Old Testament", although the books are typically arranged in a different order what what is found in the Christian bibles. Jews often have other holy writings, Midrash, which they also consider significant. Then, the next largest major collection may be the "Protestant Bible", which contains what we call the "New Testament". However, the Catholics typically also embrace the Deuterocanon, which provides another 15 "interstitial" books, containing pre-"New Testament" content (some of which may be after the "Old Testament" books.
Islam comes along and we get the Quran, which acknowledges the Jewish and Christian texts but does not endorse treating those older texts as having full accuracy. In a nutshell, Abraham had two sons, one of whom I will title the Son of Promise, through whom God's promises were made. The Jews say that the older son, Ishmael, was born from implementation of a rebellious plan, so the younger son Isaac is who the Jewish line follows. The Quran follows the older son, Ishmael.
Of course, then there are additional books, such as the Book of Morman used by the LDS church, Mary Baker Eddy's "Science & Health with Key to the Scriptures", and Seventh-Day Adventist's Ellen White who wrote the Conflict Series of books. Both Mary Baker Eddy and Ellen White are key women who wrote a bunch of material, and each had a publishing house essentially set up to help that author's material be further spread.
Then, there are the apocrypha - even more books that some people accept, and others don't. Undoubtedly, some apocrypha is known to have been dishonest about who wrote it. But which apocrypha? Is any of it trustworthy? There are some more questions that people may have different opinions about.
Does the Bible in itself talk about and name these branches, or were they created much later, long after the Bible had been finished and spread?
No. The bible does speak of a split between Peter and Paul, but those leaders resolved their differences (as recorded in the bible). As mentioned before, the bible mentions some of the Jewish branches that existed. There is some biblical prophecy that some people will interpret as referring to religious people being non-unified, but such interpretation may be rather non-universal, and the bible certainly doesn't provide names for all the various sects/denominations of Christianity.
I find that the more basic my questions are, the more vague are the answers.
Well, one way to remain accurate is to be vague. As you leave the realm of being vague, the specifics will often introduce details that will be less universally agreed upon. there are books that provide lots of specific details.
People would call such writings "doctrine" that may be widely disagreed upon by other people who don't accept some of the same narrow teaching.
So if you ask broad questions, you're likely to get some vague answers. Fortunately, this website is likely to accept questions of both types (broad/vague and specific).
That's just about all I know, amazingly. (It's why I ask.)
I suppose that as you learn some more of the basic facts, you are likely to find there are yet other details that you don't know. Realize that continuing to ask questions is not a sign of lacking intelligence. Rather, such efforts to learn just indicate that you have not fully mastered all aspects of religion.