The K visa category allows the foreign national spouse or fiancé of a U.S. citizen to enter the U.S. along with their unmarried children (under 21 years old). Once in the U.S., they must file another application to receive Lawful Permanent Resident status (green card).
If you are a U.S. citizen or lawful permanent resident (green card holder) you can sponsor your spouse or immediate relatives for green cards. This is done via family-based immigrant visas. There are two different categories of family-based immigrant visas: Immediate Relative Immigrant Visas and Family Preference Immigrant Visas.