What different versions are there of the history of the Rashideen caliphs? Why?

I know there are at least two versions of the history of the first caliphs, i.e., how those people came to be caliphs: * A simplified version, where the first three caliphs were elected by popular vote, and Ali by six representatives. * A more detailed version, involving a quarrel between Umar and Ali, and Abu Bakr being elected at a meeting, which Ali wasn't invited to. Are there any more versions? Why is there no single canonical one? Are different versions supported by different groups?