“Migrant” is a term englobing “immigré” and “émigré“. It’s similar to english, see this page :

Emigrate means to leave one’s country to live in another. Immigrate is to come into another country to live permanently. Migrate is to move, like bird in the winter. The choice between emigrate,immigrate, and migrate depends on the sentence’s point of view.

“Clandestin” means someone trying to hide his illegal situation. It’s probably the case if you don’t have immigration papers (“sans-papier“). With “sans-papier” you’re just describing the situation. “Clandestin” put more emphasis on the fact that the person is deceiving or hiding from the state.