Scapula activation during pushups

So when talking about the standard pushup, I've noticed that I tend to lock tight and have little to no movement in my shoulders.  This feels stronger and places more emphasis on the front delts, but I've heard you should do pushups with a "plus" moving the scapula through full range of motion as well.

 

I'm guessing this builds more strength in the serratus, but does it actually build more strength as far as pushing is concerned?  I'm guessing so, since I'm inclined to lock down and deactivate my scapula, which helps get more reps.

 

However, when I do one arm pushups, I can only do it by beginning the movement with my scapula, moving my chest down while my arm remains straight, and moving back up while I work through the full range of motion.  So, more strength comes with active shoulder blades?

 

This is probably a stupid question, but I'm confuzzled... Anyone know?

Well my physiotherapist mentioned that the serratus anterior is largely important in stabilising the scapula to the ribcage. So more stability = less injury. Also it would be a good idea to go through the full range of motion as it can help with a stronger protraction during the planche as the serratus anterior is responsible for this. Although it might not be the only muscle for protraction it's a good idea to make sure there's no weak links.

Oh and with the one arm push ups, supposing you're not going rocky style that's fine, just push the shoulder down when you come back to the top!