Here are the examples from American Heritage Dictionary about the uses of these verbs: migrate, emigrate and immigrate.
migrate (mì´grât´) verb, intransitive migrated, migrating, migrates
1.To move from one country or region and settle in another.
2.To change location periodically, especially by moving seasonally from one region to another.
[Latin migrâre, migrât-.]
- mi´gra´tor noun
Usage Note: Migrate, which is used of people and animals, sometimes implies a lack of permanent settlement, especially as a result of seasonal or periodic movement. Emigrate and immigrate are used only of people and imply a permanent move, generally across a political boundary. Emigrate describes the move relative to the point of departure: After the *** came to power in Germany, many scientists emigrated (that is, left Germany). By contrast, immigrate describes the move relative to the destination: The promise of prosperity in the United States encouraged many people to immigrate (that is, move to the United States).
Excerpted from The American Heritage® Dictionary of the English Language, Third Edition © 1996 by Houghton Mifflin Company.