Nothing builds shoulders like heavy overhead pressing. Anyone who presses 300-plus pounds overhead for reps, seated or standing, is going to have big, strong shoulders. Two simple grip changes will help you get there.
This means not having the thumb around the bar. You'll feel much stronger with a thumbless grip. It allows for a better path of the bar by bringing it in slightly closer to the centerline of the body. The thumbless grip is also easier on the shoulders in general and more kind to the wrists.
I do my pressing with a relatively close grip and my shoulders thank me for it by not aching anymore. Start with a shoulder-width grip, or at least in that range. As a visual cue, rotate your hands back towards your delts. Go ahead and do it right now. If your thumb grazes the outside of them, you're in the right spot for powerful, pain-free pressing.