What is the difference between the slaughter of a Muslim and the slaughter of the People of the Book?

The Shaykh : However, in my opinion, it is necessary to distinguish between the slaughter of a Muslim and the slaughter of the People of the Book. The People of the Book, by the explicit text of the Qur'an and according to the interpretation of Ibn 'Abbas: "Their slaughter is lawful." But is it a condition in their slaughter that they mention the name of Allah over it, or is it not a condition? There are two opinions among the scholars. The one I see—and Allah knows best—is that it is not a condition. The basic condition in the slaughter of the People of the Book is that it must be a slaughter and not a killing; why? Because when a Christian mentions the name of Allah over the slaughter, the Allah he refers to is, in his belief, the third of three. Therefore, his mention of it defiles the slaughter with the shirk (associating partners with Allah) that he carries in the depths of his soul. For this reason, whether he mentions the name of Allah or not, in reality, it is the same, because it is not the name of tawhid (the oneness of Allah). Therefore, I say that regarding slaughters coming from Western countries: the important thing is that it was slaughtered and not killed by a killing. As for whether they mentioned the name of Allah over it or not, that is not what concerns us; because if they did mention it, they have committed shirk. However, Allah (Mighty and Majestic) has made an exception for their slaughter, just as He made an exception for the marriage of their daughters and women, distinguishing them from the polytheists. It is not lawful for us to marry their women or consume their slaughter. This is my position.

The questioner : May Allah reward you with good.