illegal alien vs illegal immigrant

illegal alien

noun
  • A person who is within the boundaries of a political state without the authorization of the government of that state; a national of another country who has entered or stayed without permission. 

illegal immigrant

noun
  • Someone who has immigrated into a country by bypassing customs and immigration controls. 

How often have the words illegal alien and illegal immigrant occurred in a corpus of books? (source: Google Ngram Viewer )