I guess it comes down to this. The BACK (not the front) of your FAA license will say something very specific. Now how you "read into" that is the difference here.
The back of my 107 says "Remote pilot unmanned aircraft system". Let's break that down a bit.
Remote = means you are not actually sitting in the platform, but in a remote location
Pilot = You are actually moving sticks back and forth to make the platform do something
Unmanned = Again, you are not actually sitting in it
Aircraft = Yes it is a flying platform
System = A system is a regularly interacting or interdependent group of items forming a unified whole. (according to Wikipedia)
I also hold a multi engine commercial instrument rating, CFI, and rotorcraft-helicopter. And no where on the back of my pilots license does it say remote or unmanned.
As someone stated earlier that as long as you realize that the difference between the two is where are you sitting when you fly your platform, you will understand what kind of pilot you are. You are either a Remote Pilot or a Pilot. They are not the same but do the same thing. Manipulate a platform to go up and down and side and side.