Mishnayos Chullin Perek 1 Mishnah 4

השוחט מן הצדדים – at the side of the [front-of-the] neck–throat

שחיטתו כשרה – and even also ab initio, and since it is required to teach [in the Mishnah] "המולק מן הצדדים"–”He who pinches the bird’s neck with the fingernail from the side”, it also teaches, "השוחט" –”he who ritually slaughters” – post facto.

המולק מן הצדדים מליקתו פסולה – that concerning the pinching of the bird’s head, it is written (Leviticus 5:8): “[He shall bring them to the priest, who shall offer first the one for the sin-offering,] pinching its head at the nape [without severing it],” that is from its back.

השוחט מן העורף שחיטתו פסולה – And these words [indicate] that he (the ritual slaughter) did not restore the organs (i.e. the windpipe and the gullet) at the back of the neck but rather cut the nape [up to a point] where he reached to the organs (the windpipe and esophagus), for prior to his arriving at the organs, it [an animal] has been made organically defective [ritually for use] with the breaking of the neck, and even though that with the pinching of a bird’s neck, it is fit for use, there, it is such that all of it, from the beginning to the end is from the pinching of the bird’s neck [only – and not from any other ritual act of slaughtering] and it is like a ritual slaughterer who perforates the gullet little by little until he completes his act of ritual slaughter. But if one slaughtered from the back of the neck, since that [act of] slaughtering is not perfect, one cannot have the breaking of the neck from the slaughter, and it is ritually unfit–defective [literally, considered “torn”]. But, one who performs ritual slaughter from the sides, as is taught at the beginning of the Mishnah, even without restoring the organs, has performed the ritual slaughtering well prior to severing the neck.

המולק מן העורף – not really the neck, that is what there is from the slanting of the head from the back [of the neck] with the face, for it is written (Leviticus 5:8): “at the nape” (see above), but rather, opposite one who sees the neck, that is, behind the neck, he pinched the bird with a finger-nail and cut the flesh and the neck until he reached the organs (i.e. windpipe and esophagus).

מליקתו כשרה – As this is, ab initio, the commandment of pinching of the bird’s neck. And since the Mishnah teaches "השוחט מן העורף פסולה" –whomever performs the act of ritual slaughter from the back of the neck is invalid, and even post facto, it [the Mishnah] also teaches [concerning] one who pinches [the bird’s neck] post facto.

השוחט מן הצואר – under the throat is called the neck, and that is the method of most ritual slaughtering.

שכל העורף – all of the edge which sees the back of the neck (but not the back of the neck itself).