you most likely only need 1 type of overhead press. A traditional military press is a strict press where your heels are touching, and toes pointed out. Typically though, people don't do them this way anymore.
I personally don't like seated overhead presses, as they put a lot more pressure on your lower back (not in a good way). Standing overhead presses might be referring to the bar starting on your back, like a squat, and pressing that way. People with good shoulder flexibility can do these. People w/ bad flexibility should avoid these.
It depends what your goals are i guess. But, if you want a good overhead press, you need strong shoulders, and strong triceps. You don't even need any sort of raises if you're doing overhead presses. I would throw in maybe some face pulls, or rear delt raises though.
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