Every rental consists of borrowing but not every borrow is a rental. Borrowing means that you are going to return it or something equal to it. Renting means you are returning it AND paying a fee.
So to borrow a cup of sugar is correct, ONLY if you return an equal amount of fresh sugar at another time. If you return the sugar AND some of the cookies you made, you technically rented that sugar:)
So how about money... if you borrow money and pay it back - good for you:) You are a borrower. If you pay it back with interest, you are technically a renter.
On the flip side, you are a lender in either case- but when you accept payment you are also a banker, or a proprietor, or a rentee?
Borrowing is not about free- its about frequency