Is the intention of the one paying the expiation (kaffarah) that it is for delaying the making up of fasts sufficient, even if the receipt from the charitable organization indicates that it is an expiation for an oath (kaffarat yamin), knowing that the quantity and number of needy people are identical?

The questioner's intention to pay expiation for delaying the making up of fasts is valid and sufficient, as long as it reaches the poor. Its classification by the charity as an expiation for an oath does not harm it, because what matters is the intention of the questioner, and the charity is merely an agent.