And I just pointed out that you don't have to refer to migration in relation to countries at all.
"Immigration" and "emigration" are terms that are oriented toward the places/populations through which a migrant travels.
"Migration," on the other hand, is a term oriented toward the migrating person/people and the idea of origins and destinations need not be referenced within the terminology.
"Migrant" is a better term to use when you don't want to imply anything about 'leaving' or 'joining' a group/place you're migrating to or from. E.g. you could migrate between two places without becoming an 'emigrant' or 'immigrant' of either, i.e. because you may return to either at any time or travel someplace else without leaving the other two.
In short, you don't have to define yourself in relation to the place(s) you live, although the terms, 'emigrant' and 'immigrant' are oriented toward doing so.