Well, not quite the same.
Pink Slime is a title only applied to Mechanically Separated Meat, especially of the chicken variety.
There are laws in place to prevent the sale of Mechanically Separated Beef from being sold to consumers, at least in the US. So, no, that is not what is going on with the meat in hamburgers.
But it is close - it is various scraps as well as whole cuts, I'm sure McD's actually has contract for large portions of whole butcher product, probably entire output of some butchers, not just the leftovers. McD's is too big to survive on leftovers I reckon. Leftovers is common for animal feed as well, especially pet food and treats, so the market already supports leftovers from most butchers.
For what scraps are used, it never gets as close as the various mechanically recovered processes utilize, so you aren't getting the small bits of connective tissue that cling to bones.