Definitions from the U.S. Internal Revenue Service and Homeland Security.
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Citizenship: All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and the State wherein they reside. (14th Amendment to the U.S. Constitution)
Naturalization: the process through which a lawful permanent resident applies for U.S. citizenship.
Alien: An individual who is not a U.S. citizen or U.S. national.
Immigrant: an alien who has been granted the right by the USCIS to reside permanently in the United States and to work without restrictions in the United States. Also known as a Lawful Permanent Resident (LPR). All immigrants are eventually issued a "green card" (USCIS Form I-551), which is the evidence of the alien’s LPR status.
Nonimmigrant: an alien who has been granted the right by the USCIS to reside temporarily in the United States. Each nonimmigrant is admitted into the United States in the nonimmigrant status, which corresponds to the class of visa with which, or purpose for which, he entered the United States (e.g., a foreign student may enter the United States on an F-1 visa, which corresponds to the F-1 student status in which he was admitted to the United States).