As I said, A lot of the time the stuff is centrifuged to remove fat, in which case it’s used as filler.
It’s the same product, it’s just processed more, but it’s taken off the carcass the same way, and you still get to enjoy that lovely spinal cord. Colloquially the full fat product is “white slime” and the centrifuged and ammoniated product is “pink slime”.
It is not the same product, at all. The linked Wikipedia article that you posted quotes the USDA regulations which are clear that mechanically separated beef is not permitted for human consumption.
On the contrary, "pink slime", or lean finely textured beef, is made from the scraps and leftovers of (non-mechanically separated) beef, and is put into ground beef for humans.
It’s the same product, it’s just processed more, but it’s taken off the carcass the same way, and you still get to enjoy that lovely spinal cord. Colloquially the full fat product is “white slime” and the centrifuged and ammoniated product is “pink slime”.