Are force carrying particles always virtual particles? Of course we have real (i.e. non-virtual) photons, but when photons play the role of "force carrier" are they virtual? Same thing for gluons. Real gluons have been detected, but when playing the role of force carrier, are they virtual?
Something seems wrong with this picture. For e.g. 

In the nonperturbative lattice approach to quantum field theory, virtual particles are completely absent, another proof of their unreal, ”virtual” nature.

Reference https://www.physicsforums.com/insights/misconceptions-virtual-particles/
 A: At the particle level, i.e. a particle as defined in the standard model, force is dp/dt, momentum transfer during the interaction.
In quantum field theory as depicted with the Feynman diagrams, this dp/dt is transferred by virtual particles from the input particles to the output particles.
The particles are called by their name because they carry the quantum numbers of the name and the propagator representing them in the integrals has their mass, but the real fourvector assigned in the integral to the virtual particle is off mass shell and varies during the integration. QFD has higher order diagrams  for the interactions, which have to be calculated according to the accuracy required, as it is a perturbative expansion.
The "virtual" attribute is specific to the Feynman diagram representation.
All internal lines in a Feynman diagram are force carriers, i.e. transfer dp/dt by construction,not only the gauge bosons. See the diagram for compton scattering for example.
Lattice QCD goes for direct solutions on the lattice, and therefore the concept of  virtual particles is not necessary.  It is a different calculational approach , although the article involves quark propagators in the calculations.
