Technically it doesn’t (as it means condominium which in theory could be single family homes) but practically it almost always means an “apartment you own” though sometimes “half a duplex” or similar proportions of a quad or six plex style.

But in the US it usually implies neighbors above and below and on the sides.

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simianwords a day ago | parent [-]

I'm more curious now: what sort of apartment does not have neighbours nearby?

	▲	bombcar a day ago \| parent [-]
		It’s the above and below; most people in the USA will think “condominium tower” when you say condo, but some (rarer) are much more like duplexes or single family homes.