What determines an opening continuation vs an opening varation? Are these determined from historical play?  For example, when the English was first played with 1. c4, why was the English in this case determined to just be 1. c4 and anything afterwards is considered a variation?
The original distinction was mainly so that chess players have a common vocabulary (for teaching, discussing, kibbitzing) there is the concept of a "main line." Other reasonable continuations are said to be variations. This helped the teachers and the players to learn the opening lines.

Yes, history did play a role in what was considered the main line, and which options were variations. Very often, variations would be given the name of the GM who first played it as a novelty, or the one who plays it very commonly to good results. (Remember, this was in the days when most people learned about games printed chess magazines that showed up several weeks after a game was played.)

These days, thanks to very powerful chess engines and massive databases, the mainline is arguably simply the line that is the most frequent continuation (played by those with high ELOs.) 

It is also important to remember that as more games are added to the database, the mainline tends to shift to other moves, especially as refutations are discovered by the opponents.

Hope that helps.