You’re correct. They are the same. Loan may also apply.

However, depending on where you are, there are regional differences in where the terms get used. Locally, you rent an apartment but lease a warehouse (why?). Also, if you rent an apartment and turn over your lease agreement to another person, you are sub-letting the apartment. And “let” also means lease in this context. Err rent. Fuck, I’ve gone cross-eyed