You buy a share. You now rent it to someone else. They sell the share again (and hope to buy it back later at a lower price). Same share has been sold twice. The 2nd buyer of that share can then rent it again to another seller which increases total short interest.

Yes. If I short a share, I’m selling the share to someone and planning to buy it back later. That person who bought the shares from me can then lend them to someone else... so now two shares are being shorted when only one real share exists.

So, closing the loop back to the original analogy, you shouldn't be able to sublet an apartment with an occupancy rate of 4, out to 8 people.

Correct. It's akin to fractional reserves [https://www.thebalance.com/what-is-fractional-reserve-bankin...]