They are all real estate properties. You rent or purchase a property. When that word is used for where a person lives long-term it’s not potentially meant to denote ownership, but just a place of residence that they spend some of their money to do so.
Honestly not purposely trying to stick a finger in someone’s eye over this, that’s just the generic term for a place that people live in/at.
I’ll tell you what though, next time I’ll try to remember the use the word ‘residence’ instead, though that’s not completely accurate either, because somebody could just be living at a friend’s place and not spending any money to do so.