"Calling a cat, a cat", as we say in French: I really do not see what anyone would lose just putting the right words on each action -- and it's not even very difficult to define.

Can the user use the thing mostly without the provider? Yes = purchase, no = rental.

If all of sudden it's all "rentals" everywhere, what does it change -- apart from opening up an avenue for the people willing to actually sell the things they would otherwise lease, because consumers will prefer it that way?