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.
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.