Feature parity is not really a goal of these products - they are totally separate teams, technologies and languages. If one team develops something awesome then of course the other will try to reimplement, but it's not really the case that features "hit cloud first".

Bitbucket Server (formerly Stash) is a completely different codebase from Bitbucket Cloud. They share zero code. One is written in Java, the other in Python. It's a constant source of confusion. The naming is because of a terrible marketing decision. Atlassian marketing does all kinds of weird things, like advertising Bitbucket as only supporting git despite also supporting mercurial.