An inmate is a person who lives in a specific place, especially someone who's confined there, like a prisoner. You can call yourself an Inmate if you get sent to your room, but usually inmates are behind bars in "the big house."
You can talk about a hospital inmate or the inmates at a local boarding school, but it's most common to use inmate and prisoner interchangeably. Originally, in the 16th century, an inmate was "one allowed to live in a house rented by another" — a roommate who's not on the lease, in other words. This meaning comes from in and mate, "friend or companion." By the 1830s, inmate had come to mean "one confined to an institution."