Usually, VPS is taken to mean the virtual private server that is rented at some company, not one of the virtual machines you host on the physical hardware that is located on your private property.

It's real simple, if you don't own the hardware, if it's not physically available to you to go whack with an axe, then you don't own anything, you're just renting and entirely at the mercy of whoever you're renting from.

self-hosting doesn't mean you have to own the hardware?

Also, "owning" and "being able to walk over and physically whack it with an axe" are not the same thing. Servers can be leased, and there is something called "server housing" which breaks your analogy

yea, it does not, because people are using the word wrong..

Saying you own your leased server is the same as saying you own your rented apartment or leased car.. It's not yours if it's someone elses, in the same way the movies on netflix are inherently less yours than the movies on your laserdiscs, dvd's or blu-rays.