I just felt the urge to post this very old joke:
The Military Press
There is very little consistency of terminology in the fitness industry. Depending on the author of a program, a military press might be called an overhead press, a shoulder press, or something else. I wouldn't even assume you'd be seated for a shoulder press unless the program specified a
seated shoulder (or overhead) press.
I agree with Alco too. I much prefer push presses, barbell or dumbbell.