The Basics
Here are the main types of immigration statuses:
Citizen
includes the right to vote and run for public office.
Humanitarian Options
Depending on the situation in the US or the country of origin, options may be available.
Deferred Action
A temporary relief from removal and employment authorization.
Legal Permanent Resident (Green card)
Allows someone to stay in the US and petition for certain family members.

Non-Immigrant Visas
There are a variety of non-immigrant visas including tourist, student and work visas.

Undocumented
Someone that does not currently have a lawful immigration status in the US.