Read the definitions below. Maybe they will help you understand the difference.
No, you can't. I sure hope you aren't teaching all this misinformation to your students.
Immigration Terms and Definitions Involving Aliens
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. LPR’s who are awaiting the issuance of their green cards may bear an I-551 stamp in their foreign passports.
Nonimmigrant
An alien who has been granted the right by the USCIS to reside temporarily in the United States.
Illegal Alien
Also known as an "Undocumented Alien," is an alien who has entered the United States illegally and is deportable if apprehended, or an alien who entered the United States legally but who has fallen "out of status" and is deportable.
An undocumented or "illegal alien" is an alien who entered the United States illegally without the proper authorization and documents, or is an alien who once entered the United States legally and has since violated the terms of the status in which he entered the United States or has overstayed the time limits of his original status.