A better analogy is sports encompasses basketball and football, so basketball and football are synonymous with sports.
But you don’t know anything about sports, so that’s probably a bad example too.
C'mon, BB, don't dig in on this.
Are you maybe using "synonymous" idiomatically? Like something along the lines of, "ESPN is synonymous with excitement!"?
"Synonymous" means "equivalent" or "having the same idea".
"Encompassing" (as it's used here) means "includes totally".
Think Venn diagrams. Or not since I'm way too lazy to find pic's representing this idea.
How about this:
Just because B is a subset of A does not mean that B is the equivalent of A. (Because there is a whole lot of A that doesn't have shit to do with B.)