Like many solitary predators, cats are territorial. This might sound a bit strange, given that they tend to pay precisely zero rent, and, indeed, often actually cost their owners more in security deposits. But, in general, cats do understand the concept of territory and space, marking their own and fighting interlopers when they feel threatened.
What might make this entire thing somewhat difficult for humans, is the fact that cats, particularly outdoor cats, might decide that someone’s house is now theirs and never mind that this person isn’t even their owner. However, as this list shows, many cats are at least quite chill around humans, which is fortunate, since they will literally fight, tooth and nail, for their own territory.
If you are particularly unlucky, the cat that isn’t yours but is in your house will do its best to make it their own home with the cat legal code, i.e. marking their territory with urine. In best-case scenarios, the cat is marking just by walking around, as their paws have scent glands that other cats can detect. The fact that you can’t detect them doesn’t appear to make any sense. However, some male cats will also pee on your property, just to let you know who is in charge.
Actual cat owners will note that, unlike most of us, cats really do like to use the entire three dimensions of space in the room. While we mostly sit on some objects mere feet from the ground, cats will “guard” their territory from the highest point they can find. If some of your items need to be pushed aside, then so be it.
Interestingly, one factor that might push cats into “your” territory is competition with other cats. After all, hunting grounds, shelter, and water sources aren’t something cats like to share with their feline compatriots. So, in a sense, the “feline distribution system” might almost be a real, ecological phenomenon, where certain cats end up “pushed” into the hands of a human.