What is the difference in the method of distributing Zakat al-Mal and Sadaqat, knowing that both are distributed to the poor, the needy, and those in distress?

The difference between obligatory Zakat and voluntary charity (Sadaqah) is that Zakat has specific recipients, as stated in the verse: "Indeed, [obligatory] charities are only for the poor and the needy, and those employed to collect [zakah], and for bringing hearts together [for Islam], and for freeing captives [or slaves], and for those in debt, and for the cause of Allah, and for the stranded traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise." (At-Tawbah: 60). It is not permissible to spend it on anything else.

As for voluntary charity, it is permissible to spend it on all charitable causes. It can also be given to a non-Muslim, unlike Zakat, which is not given to non-Muslims, nor to those whose maintenance is obligatory upon the giver, nor to the wealthy, nor to Banu Hashim. Voluntary charity may be given to the Prophet's household (Ahl al-Bayt), unlike obligatory Zakat.