The fact that the concept of force is purely an abstraction is lost on many people, including many engineers and physicists. We’re so used to seeing “force” as a blue arrow acting on a pink potato in physics and mechanics texts which causes a body to accelerate or exert a reaction on another contacting body that we don’t, or rather, are conditioned not to really ask what a force is but only how it works. As students go from basic physics into E&M and relativity theory, we then start discussing in detail the concept of a force being a field with curvature that exerts a bias on the inertia of an object in the field such that it tends to want to go in a particular direction (along the geodesic curve mapped onto the underlying metric). However, fields are just as much of an abstraction as forces are; there is (as we currently understand it) no medium for the conveyance of electromagnetic waves, and thus no identifiable or visible field of anything that is disturbed by the wave that is passing through. We can only measure the field via its effect on other objects and waves. Similarly for gravity, and the range of the strong and weak forces are such that we can’t even measure their effects directly, and they are simply inferred. Classical and relativistic field theories are also (mostly) continuous; the field strength varies as some function of distance from its source (for EM fields, a charge; for gravity, a mass) and is smooth except in particular cases where a defined boundary exists, such as the event horizon of a black hole.
In quantum mechanics, however, an entirely different epistemological approach is used; QM ignores the business of forces and fields as real phenomena and instead presents all mechanics as metered interactions or exchanges between systems. The EM force is no longer a smooth metric field in its own invisible, self-sustaining plenum; instead, it is the result of exchanges of “virtual photons” between two electrons. These virtual photons are “force carriers”, which transmit what end up being measurable impulses between two systems. Similarly, what were formerly known the nuclear forces (at one point, the strong and weak forces) are now understood to be fundamental interactions between particles mediated by force carriers (gluons and W &Z bosons respectively, or in the case of the nuclear binding force (a.k.a. the residual strong force) it is an apparent result of these interactions. What we measure as the result of forces is actually just an accounting of the mechanics of fundamental particles. The difference isn’t in the result but how we model the interaction.
Now, stemming from the desire to do something useful with QM are a set of hybrid theories called quantum field theories (QFT). The most famous of which is quantum electrodynamics (QED), which was entered into the public consciousness by one of its most notable developers, Nobel laureate Richard Feynman and his eponymous diagrams. (It should be noted that while Feynman is most widely noted for being associated with this theory, he stood upon the shoulders of others in developing it, and in particularly the great mentor to dozens of notable physicists, John Archibald Wheeler.) QED is (as one popular book by Feynman is subtitled) “The Stranger Theory of Light and Matter”, and explains among other things why light is refracted and reflected differently by different materials. The basic theory is conceptually easy to understand but ferociously complicated to implement in a formal fashion, and Feynman’s most notable contribution is what mathematicians would call a cheat; he basically summed up all the infinitely different paths a force carrier can take, and then cancelled out the infinities by a processes known as renormalization which basically lumps together different categories of paths, and leaves a finite result that can actually be used to predict something useful.
The net result is that while QM gives some very fundamental rules about interaction that happen on a level to small for us to actually measure, quantum field theories allow us to use QM to predict interactions that are close enough to the macro scale that we can observe to be useful. And predict it did; QED has offered the most precise predictions ever measured (specificially, the Lamb shift). This doesn’t mean that the fields in QTFs are “real” in any sense more physical than providing a mathematical convenience of predicting the correct result; they simply allow for the ability to apply the mathematical formalism of QM to a larger scale interaction, the same way in which the assumption of a fluid mechanical continuum applies to a flow field that is actually comprised of a viscous collection of individual molecules. The theory works well enough accurately model the resulting large scale behavior (at least, in certain regimes) but the physicality of the situation is that a fluid is actually a collection of co-interacting particles.
Getting back to the o.p.'s question, I can really clarify what ZenBeam has already written other than to say that the Pauli Exclusion principle isn’t due to any exchange of force carriers but instead is just one of a number of fundamental rules about how particles can interact and share the same locus. You can have any number of photons in the same quantum state (and, like the Holy Trinity, they may even be one and many at the same time…how messed up is that?) but not the same with fermions. This manifests itself on the macro scale as EM forces (because you can’t shove an electron into an already occupied orbital) but it is really just a fundamental accounting rule in quantum mechanics.
On the topic of fictitious forces and the abstractions of forces and fields in general: so-called fictitious forces are real (as far as the subject is concerned) but simply dependent on the reference frame in which they are acting versus fundamental forces which should be the same regardless of the frame of reference. However, even what we regard as fundamental forces like gravity can be abstracted into a reference frame outside of which it simple appears to be a force. This whole business with forces and fields is a convenient and workable way to apply the rules of mechanics, but it doesn’t mean that there is a pushing arrow or a warped grid that causes these mechanics; they’re only a sort of mathematical or conceptual language in which to describe the impetus for motion and reaction. This vying between fundmamental Platonic-Aristotelian view of the world as being a real manifestation of fundamental rules, and the more empirical view of science as a study of real phenomena in the natural world championed first by Philoponus remains a key tension between competing epistemological views of fundamental physics today.
Stranger
Couldn’t resist!