Have you noticed how the media have begun to use the word "migrant" in their reports of those assembling at Calais and making their way across the Mediterranean? This displaces the previous "immigrant" which used to be used for incomers from abroad. Emigrants, on the other hand, were those who left for abroad.
It remains unclear if "migration" will replace immigration or emigration. Migration is of course more commonly used to describe the temporary seasonal movement of animals, birds and whales. So I suppose it would be less than accurate to use it to describe the more or less permanent movements of human beings.
Much the same applies to the verb "migrate". (Although, curiously, while "to emigrate" was common enough, "to immigrate" was seldom used.)