A highrise just means any tall building, with enough floors to make an elevator required.

Housing highrise buildings can either have apartments for rent, or condos sold outright (usually with some kind of a homeowners association that takes care of utilities, trash, etc that you have to pay recurring fees to).

In my country (the US), highrise condos exist but are much rarer than every other form of housing. In Spain I saw a lot of highrise condo buildings, some of the condos even had two floors. Imagine a mansion inside of a highrise building, pretty neat.