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:


*

*Does this classification work? 

*Is it exclusive and comprehensive? 

*Is it used in some way?

*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.
 A: You could say that there are currently as per the Standard Model (SM), force mediators. Photons (electromagnetic), gravitons (gravity), gluons (strong force), W and Z bosons (weak force).
You could say that there are as per SM some particles that can actually emit these mediators, so electron for the photon, quark for the gluon (but the gluon emits its own type too) and the graviton (theoretically emitted by all particles), and the W is the mediator for neutrino absorption and emission and the Z is the mediator for the momentum, spin and energy when neutrinos scatter elastically.
https://en.wikipedia.org/wiki/W_and_Z_bosons
But with this, we have not covered all particles in the SM, for example, based on this you could not classify the Higgs boson as either mediator or emitter (it is a very good question though whether the Higgs boson would emit gravitons).
https://en.wikipedia.org/wiki/Higgs_boson
A: Please note that the concept of "force" comes from classical mechanics. Fortunately there is the definition of force as $F=dp/dt$, $p$ the momentum in the interaction, which is exactly what is needed in Feynman diagrams. Every virtual particle exchange carries a dp/dt, and the four vectors are what are used to calculate the probabilities of any interaction or decay at the quantum mechanical level of particles. example:

There is a force carried by the virtual electron in these two Feynman diagrams.
We do call fundamental forces and assign a gauge boson unique to these  , the strong(gluon), the weak , (W and Z), the electromagnetic ($γ$).  Gravity is not at this time quantized except only effectively.   Usually the lowest order scattering between particles in these forces is  with the exchange of the gauge boson. 
The use of the concept of "force" in the quantum frame is useful when thinking of the strength of interactions, as the table linked shows. The four forces are distinct in the coupling constants characterizing the Feynman diagrams that model the interactions.
