Agreed.

An expat is someone "on assignment", who has and expects strong ties with their home country. People who fit this description tend to frequently seek help from their own consulates, for example. It's particularly relevant for Americans because we tax ourselves even when overseas.

An emigrant (as seen from the source country) or immigrant (as seen from the destination country) is someone who has (usually permanently) moved and now expects primary services and sovereignty from their new home country.

I highly doubt that the distinction is strictly an anglophone concept, although perhaps it's related that they sound similar and have similar roots.