After I get off my 9 to 5 clown shift most day's, I'll include push pressing off of a set of power rack pins.
When the bar is resting on the heals of the hands, rather than in the palms, than the wrist is in direct line with the bar & forearms. This allows better inline leverage and usually more weight used in the exercise (power). That is the kind of pushing action I think your referring to. When the bar is resting in the palm of the hand, as in regular pressing, too much indirect stress is put upon the wrist and forearms themselves. This exercise is usually done standing with a slight heave and knee jerk each rep. It can be a power movement and prime shoulder mass builder. Probably the main cause of the shoulders being so sore. Welcome to the Big Boy's exercises. Good Luck.