Yes different nations all have their own pedantic legalese on what constitutes a 'migrant' but if someone physically moves from one country to another long-term they are objectively a migrant

Here's a dictionary definition of the term:

A migrant is any person who moves away from their usual place of residence, either across an international border or within their own country, to live somewhere else

i.e. one who has migrated(Migrated is the past tense and past participle of the verb migrate, meaning to move from one place or region to another)