DRAE
Carta de pago
Documento en que el acreedor confiesa haber recibido el importe o parte de la deuda.
Therefore, I think carta de pago is indeed acquittance or proof of payment.
The paying-in / deposit slips to which Janet refers are called in Spain Talones de Cargo.
The method is as follows: the authority gives you both a Talón de Cargo (that tells the Bank what to do with the money, and that sometimes is called "Ejemplar para la entidad colaboradora", i.e., the Bank), and a Carta de Pago, which, duly signed / stamped by the Bank, is the document that acts as proof of payment.
You may get a clearer idea with the following Form, which is actually the same form with four different uses / names: For the Taxpayer, For the Treasury Department, Acquittance (Carta de pago) and For the collaborating entity (Para la entidad colaboradora; this would be the Talón de Cargo / Paying in slip; in fact, in the guidance notes of the form, it is called a Talón de Cargo, and not Ejemplar para la entidad colaboradora).
Reference: search for Modelo 620 de la Agencia Tributaria. It seems that I can't link the page, as I am a newbie here.