Can elementary particles be nicely classified into "force transmitters" and "force emitters"?

This well-received answer begins with

First of all, you can't compare photons with electrons. They are different types of particles (spin 1 vs spin1/2; force transmitter vs force emitter).

I'd never heard of assigning a binary distinction of whether a particle emits a force, or transmits one, so I'd like to ask the following:

1. 
   

   Does this classification work?

   
   


2. 
   

   Is it exclusive and comprehensive?

   
   


3. 
   
   

   Is it used in some way?

   
   


4. 
   

   Are force emitters always also force responders?

   
   

At first I thought that there may be some interaction between photons and gravity that blurs the line, but then again perhaps gravity just affects the space that the photons propagate in rather than deflects the photons themselves.