I think the last 10 years with numbers being what they are, teams are just happy to get their kids games regardless of how you label it.
I have seen some things like Leo JV vs Rita Frosh. Or a team that has a soph team playing against a true JV team that may have juniors (and even seniors) who don't play much on varsity. Overall, I think most programs are happy to just to have a game for their lower levels regardless of the technicality. I know it used to be frosh vs frosh and soph vs soph at all the bigger programs. But now I feel like "JV" is more widespread than "soph."
I think it makes more sense to play frosh and varsity Friday and then JV Saturday or Monday so programs can add the juniors/seniors who didn't play Friday to the list of sophomore to get a more inclusive JV game.