Learn English – Word to describes the money that you lend to somebody

Lend and borrow are fine for very nearly all cases (there may be specialised terms for corporate finance, although even there companies borrow money from banks which lend it).

You can make a repayment (as you mention), and someone can make a repayment to you: you can say "He's repaying the loan I made him; I've received a repayment from him." Just as the word loan is used for the money which changes hands when someone lends it, repayment is the sum of money which moves in the opposite direction.

However, while repay is obvious for make a repayment, having looked at a number of resources I can't find a one-word synonym for receiving a repayment. There are words which indicate forcing the repayment of the loan: foreclose and reclaim, for example; but the simple act of receiving a sum of money someone is repaying doesn't appear to have one. Receive isn't specific enough¹.

¹ The head of a Customs Office in the UK is called a Receiver, because it's his office which receives customs dues. Similarly the Metropolitan Police used to have a Receiver who was responsible for the funds received from central and local government.

This is an excellent question. But, I do not believe that English has a sense of a difference between the two concepts.

Borrow and lend are opposite sides of the same equation. To lend is to allow someone to borrow. To borrow is to take someone else's loan.

I think you will have a greater peace with the idea if you think of borrowing money (or other valuable commodity) as being a loan of the fiat value of the money, and not the cash itself. Hence, you are returning the same item.