How does double spending work?

Question

bitcoin

Why does double spending work in such a way that a person must send exactly two transactions? Everywhere it says that a person sends two transactions, the blockchain forks, one transaction on one side, the scammer needs on the other? Isn’t it enough to pay for some service, to fork the blockchain so that the alternative branch is confirmed, where there is no fraudster’s transaction, but with a transaction for the service, to be in the unconfirmed branch? So that there is no extra transaction of the second, isn't that enough?