Diplomatic Territory is divided into 3 types:
Friendly: Territory owned by your civilization. Friendly territory can also be established by becoming allies with a major civilization, or by becoming the Suzerain of a city-state. Units will heal faster in territory that is friendly to them, as well as take advantage of special abilities and policies associated with friendly territory. Units must be in friendly territory in order to be upgraded.
Neutral: Territory that is not currently owned by a civilization or city state. This territory may be claimed by a civilization or a city state, through expansion of city borders or by founding a new city there. With the exception of the Fort and Airstrip improvements, players are not allowed to construct items in neutral territory.
Rival: Territory that is owned by another civilization or city-state. Players cannot move into a rival’s territory without first establishing Open Borders with that civilization. Unit healing is lowest in rival territory.