I've certainly heard American Catholics call it "Communion" as well. But that's a very minor point!

Sure, both are used. That's why I said "imply" since it's much less common. Same with "our father" vs "the Lord's prayer".

I was raised Catholic with a mom who said the rosary every day and everybody we knew called it communion. The term Eucharist was only used by the priests etc during Mass.

I've only ever heard it called communion, unless the discussion is among theologians.