An illegal alien is someone who doesn't.
Yes, thanks.
My wife was a legal immigrant to America and is now a naturalized U.S. citizen, so I am well aware of the difference.
"Immigrant" implies legality, or at least the intention to stay in some other country for a very long time. Normally that's a tenuous situation when one is in a country illegally.
But given that our federal lawmakers (right up to GWB himself) do not give a damn who is in America, and contantly pose schemes to excuse their criminality, it may very well be that "immigrant" is the proper word. Though still "illegal".