These two verbs - as well as immigration and emigration, immigrant and emigrant, the nouns formed from the verbs - are opposite sides of the same coin. Let's see if our friends in The Sentinel can help explain the difference.
The words derive from migrate, to move from one area to another; migrate itself comes from the Latin migrare, to change one's abode. Many animals or birds migrate north or south according to the season, following food or, especially with birds, breeding in the cooler part of their range and overwintering in the warmer part.
When people migrate, however, it's more common to use emigrate (to leave the country where they live) or immigrate (move permanently into a different country).
Emigration is usually, but not always, voluntary. At the time of the Highland Clearances in Scotland two hundred years ago, for example, many people were forcibly taken to the coast and put on ships which took them to America or Canada. There they were offloaded and abandoned, to make a new life for themselves as best they could, as involuntary immigrants.
It is, however, more common for people to emigrate in an attempt to make a better life for themselves in a new country.
"My great-great-something grandparents were immigrants," Jim said. "They emigrated from Ireland at the time of the potato famine."
"Jim, everyone except the Native Americans are immigrants," Blair told him. "Okay, not all of them emigrated from their original countries voluntarily; look at the Africans who were brought here as slaves. I'm sure they'd rather have stayed in Africa.
"Though come to think of it, even the Native Americans were originally immigrants. They came into the country twenty thousand years ago from Asia, crossing to what is now Alaska by a land bridge, possibly following migrating herds of animals, and made their way south and east until they'd settled throughout the Americas."
"That," Jim told him, "is more than I needed to know."
Remember, emigrate means exit a country to go and live somewhere else; immigrate means go into a new country, meaning to live there permanently. Additionally, according to Merriam-Webster, somewhere around 1942 someone coined the word 'in-migrate' as a possible alternative to 'immigrate'.
Sources
http://www.thefreedictionary.com/immigratehttp://en.wikipedia.org/wiki/Immigration http://www.thefreedictionary.com/emigratehttp://en.wikipedia.org/wiki/Emigration http://www.thefreedictionary.com/migrate