When it says "Press", does that mean a military press, bench press, incline press or shoulder press? What kind of press is it asking for?
By definition, a Press happens when a lifter is standing up right and the bar is resting on the anterior deltoid, the lifter presses the weight overhead to lockout using his shoulders and arms. The legs must be locked and no hip movement is allowed.
The reason it is called a Press and not a Shoulder Press is what else would you use to Press the bar overhead? Your mind? It is like referring to a Squat as a Leg Squat. What else would you squat with? Hopes and dreams? Now you can see how funny it sounds to say Military Shoulder Press. But to define it, I assume Military would be a reference to standing upright, the shoulder would refer to what you use to press the bar, and the press...well you get it.
In a not so long ago forgotten time, the Olympics used to have 3 movements for Olympic weightlifting, the Snatch, Clean and Jerk and the Clean and Press. That is right fans of Olympic weightlifting, they used to let the guys do a press, it looked like a standing bench press with the angle of the back. If you search back in the CrossFit Football archives you can find a sweet picture of Coach Burgener doing a press. And in 1972, it was eliminated it from competition.
Here is a video of Serge Redding lifting 502 lbs in the Clean & Press.
If you pause the video at 50 seconds, you get to see Serge Redding leap into the air in celebration. If anyone argues that Olympic Weightlifting does not have carry over into the vertical jump needs to take a look at this video. To see a man of his size leap straight legged into the air is impressive.
Here is a link to an article Bill Starr wrote about The Press