Not really the ability to physically occupy the house is one of the rights owning it gives you. There are other ways to gain that right but there is conceptual overlap there.

In some legal systems, physically occupying the house gives you ownership rights: https://en.wikipedia.org/wiki/Adverse_possession

My tenant in the UK does not own the flat they occupy; my landlord in Berlin does own the flat I occupy. There are rules to say that landlords can’t just enter on a whim, and rent is a very common way to occupy a property.

Yes exactly, ownership gives you the right to occupy the property and you can also trade that right for rent as well as reaquire it. Hence conceptual overlap.