I would put them in three groups...at least as far as how things work around here.
Rec....meaning anyone who wants to play gets on a team
Local....they have tryouts...but are "local" based teams...meaning no out of towners. They play against neighboring towns
Travel....tryouts & travel to out of town or out of state tourneys. The tough part is there are so many levels. You've got regional (meaning concentrated in a particular part of the state)...statewide (meaning they draw from a much wider area) or National (EvoShield Canes, etc...who draw nationally.
Select & Elite were originally terms to describe different levels of competitive soccer here in Ohio.....I consider Select or Elite to be part of a name...rather than a particular "level" of play. There are a lot of teams that use Elite in their name...that are not very good. You're free to name your team whatever you like....lol