I can vouch for the pike push ups. When I injured my levator scapulae on my right side, it let me train around it because I didn’t have to lock out with my hands directly over (under?) head and I could gradually work up to that position before standing pressing again. When I got back to standing press, I hadn’t loss any strength despite not training it for 3 months.
Even now that I can do standing press again, I still include these as well and I’ve never had better front and lateral delt development. Standing press and pike press did about as well on their own, but the combination has been great and it’s not because I was training shoulders w/ more volume.
If I had to guess, I’d say it’s because they have different strength curves so doing both trains the shoulders in both a more stretched and more contracted position but not totally sure.