Green cards under the family based categories
US citizens and Legal Permanent Residents can petition (file for) for relatives. That is called family-based eligibility. If you are the spouse of a US citizen, an unmarried child of a US citizen or the parent of a US citizen (who is at minimum 21 years old) the US citizen can petition for you. You are in a category called immediate relative of a US citizen.
If you are in the category called family member of a U.S. citizen, you are one of these groups: meaning you are the unmarried son or daughter of a U.S. citizen and you are 21 years old or older, a married son or daughter of a U.S. citizen, a brother or sister of a U.S. citizen who is at least 21 years old. This means your US citizen family member can also petition for you.
To be considered in the category called a family member of a lawful permanent resident, you are the spouse of a lawful permanent resident or the unmarried child under the age of 21 of a lawful permanent resident or the unmarried son or daughter of a lawful permanent resident 21 years old or older. This means your lawful permanent resident family member can petition for you.
Only a US citizen can petition for his or her fiancé(e) or that person’s child. This is popularly known as the fiancé visa. It means you get a specific visa to come to the USA to get married to your US citizen fiancé within 90 days of your arrival.
Other family-based visas include the VAWA, where someone who is the abused spouse of a US citizen or lawful permanent resident can self-petition on the basis of that abuse. An abused child, i.e. under 21 and unmarried can also self-petition in this manner.