The 9mm you are interested in is described here
to help differentiate it from the 9 X 18 Makarov round and the 9 X 21 round.
9mm Luger, Parabellum, 9mm etc. are all the same designation but come from different origins.
The mark on the case is basically a ring to assist the case in resisting setback as the round slams into the feedramp during the chambering action.