As Richard answered, there is a difference between translations and canons. However, I wanted to add that there is also a difference in source text. This later subject is the matter of the field of Textual Criticism.
That is, nobody currently has the original autographs. What we have are copies, and often copies of copies, some of which come in fragments. For works written before the invention of the printing press, we don't have a guaranteed method of knowing the exact words of the original. However, we can make some very good guesses based upon the copies we see. There are different schools of thought on how to put these pieces together. For instance:
- Do we assume that the actual Bible was preserved by God to be
available to the general public for all periods, or was it preserved,
but in a hidden manuscript?
Do you believe that monks making copies would be more likely to be
lazy and leave a letter out, or more likely to add a letter to fit
Because of this, there are different groups of texts which make up the different source texts. This may also inform your decision on what you believe canon to be.
As for canon, there have been completed lists of what is accepted as canon going back to at least the 2nd century. Some believe the Muratorian fragment to have been written in 170 AD. But the earliest lists either don't have a complete copy or there's disagreement with the authors of the lists.
However, the subject isn't quite muddied as much as you might think. We actually know more about the Bible than we know about almost any other work predating the printing press. We have many more fragments, in much more agreement than other work. Word for word, we know more about the words in the Bible than we do about the words of Shakespeare's plays. Also, I believe that every word of the New Testament has been quoted by the early church leaders in works which have more complete copies. Furthermore, at least for the most popular canons, the most important doctrinal themes are still present in the same way. So, while there is some disagreement, and even heated disagreement, the overlap is enough that the major doctrines can be agreed upon from them. For more information on the historical textual evidence, see Josh McDowell's Evidence That Demands A Verdict.
Each denomination has reasons why it believes the canon it chooses, and I have yet to see any confusion within a denomination on what it considers canon. For some, the canon has been so obvious that they never felt the need to spell it out. I don't think that the Catholics had to spell out the canon until the 1500s, which was probably done more as a side effect of another issue. The fact that you've never heard of other canons is itself testimony to how ubiquitous the standard canon is. If you were to take away all the books that people disagree about, you would have the standard Bible that most churches, at least outside of Catholicism, consider to be the full canon.