This is something many people get confused about. When is it 'immigrate', and when is it 'emigrate'?
Let's take the fictional case of John Doe, who lives in England. He decides to go to America to live and find work. So he emigrates from England, and his American cousin says he immigrates into America. (Note: his English cousin still maintains that he emigrated.) Then he decides to go to Australia to live and find work. John emigrates from America and his Australian aunty says he immigrates to Australia (His English cousin has given him up as a bad job by now, because he never settles anywhere.)
Then back he comes to England to live out his old age. The Australian aunty, hypothetical tears in her hypothetical eyes, says he is emigrating from Australia. The English cousin (who may or may not welcome him with open arms) says he is immigrating to England.
John could also be called a migrant, because he moves all over the place.
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