So just to level set on the difference in rep ranges, read up on this.
The shoulder press is very different than the overhead press (aka barbell press and aka "the press").
The shoulder press, because you're sitting on your butt, locks out everything south of your upper back but does have an advantage in overall shoulder stability. One core area that it lacks in is weight increase, as you're usually limited to dumbbells and getting them up and down starts to get impossible if you're pushing a lot of weight around. An advantage is that you have to handle each load individually, which helps train shoulder stability and not letting the strong arm make up for the weak arm like what can happen with a barbell.
The overhead press has the weight getting loaded all the way from your wrists to the bottom of your feat. Your legs, lower back, abs, and obviously arms/shoulders are all involved. As you normally start in a rack, it's much easier to handle bigger weight and if you fail a rep it's somewhat straightforward to bring it back down, either into the rack position or the physical rack itself.
Directly answering your question, I think they're trying to keep you from max exertion (~5 rep range) on your shoulder presses because (a) it's harder to get the weight just right (b) it's harder to haul that much weight up and (c) it's easier to get a little cock-eyed in a shoulder dumbbell press and get hurt.
I would follow your program first and foremost, but in generally I don't find the time for a seated shoulder press because between overhead pressing, bench pressing, and other upper body work there's just not a lot of room for them to get tucked in. They're not bad persay, but there is better.
Again, I'd follow your program first and foremost. Good programs were put together by smart people who know what they were doing.