A permanent resident is someone who doesn't have citizen status, but may remain in a country indefinitely. An immigrant is a foreign national who has completed a multi-step process and been granted the privilege of living and working permanently in the United States. In most cases, the United States Citizenship and Immigration Services (USCIS) must first approve an immigrant petition, usually filed by an employer or relative. Then, an immigrant visa number must be available. After that, if the immigrant is already in the United States, he/she may apply to adjust to permanent resident status.
The Immigration and Nationality Act (INA) governs immigration in the United States. For the part of the law concerning most types of permanent resident status, please see INA § 245. The specific eligibility requirements and procedures for adjusting to permanent residence status are included in the Code of Federal Regulations [CFR] at 8 CFR § 245.