No. Mil-spec is an actual certified standard

Military grade is basically just “we made this shit to look like it’d be good as a prop in a movie” no actual standards, just good enough to sorta kinda sometimes work and is made as cheap as possible.

Edit; interesting comment by the other fella in the same reply chain, maybe “military grade” also encompasses stuff that’s made for specific purposes but doesn’t need to withstand rigorous standards, just be good enough for this one thing this one time and not much else

Granted, YMMV depending on country and region.