Unfortunately verbally its a confusing distinction but I agree its seems more consistent

I’ve gone from NZ -> UK -> EU

And along the way I did say I was an expat (in the UK), because I didn’t want to stay and get citizenship but instead the intention was to stay a NZer and eventually return (though also because expat felt like a British term I used it more)

Now that I’m in the EU with an intention to stay here forever I label myself as an immigrant, because of that change in intent

Just a personal anecdote, but maybe there’s some useful commentary on how people perceive it