Puerto Rico is an "unincorporated territory" of the United States.
Inhabitants of Puerto Rico are US citizens, and can move freely to the mainland.
However, Puerto Rico does not have representation in the Congress, nor votes in the Electoral College.
Before statehood, Alaska and Hawaii were "incorporated territories", following some court decisions around 1900, following the Spanish-American War.
If I understand the UK, England and Scotland are kingdoms, but Wales in a principality. What status does Northern Ireland have?