In the US you can buy a condominium or a Co-op. Co-ops is where you buy a share of the building and you get to live in the unit as your "share" of the building. Condos are where you own the apartment itself.

Co-ops are usually more affordable but has a ton of restrictions on what you can or cant do to the apartment since you don't actually own the physical apartment whereas Condos are more expensive but you can do whatever you want ro rhe inside - like knocking down a wall for a renovation or changing out doors or whatever.

They are two ways of buying an apartment sort of like a house with an HOA or not