Physicist here. I don’t buy some of these distinctions, like the chirality. Chirality is an observable, it’s like saying there are two photons because they can come in two polarizations, but polarization is not an inherent property: it depends on how we measure it. So I could describe any photon in the left/right chiral basis just as well as in the vertical/horizontal basis or any two antipodal points in the Poincaré sphere, so which is the “right one”? Neither. Spin on the other hand (which is where polarization comes from) is well-defined for any photon and it’s always 1 (the astute reader will wonder why the projection of spin 1 does not take 3 eigenvalues 1,0,-1 and it’s because photons are massless so the 0 projection never occurs because there is no rest frame for massless particles).
Chirality is a real property of (most) elementary particles. For example the electron with left chirality has a weak hypercharge of -1, but the electron with right chirality has a weak hypercharge of 0. https://en.wikipedia.org/wiki/Weak_hypercharge#Definition In some sense, they are very different particles. Also, only the left version interact with the weak interaction.
Ah, then I was thinking about helicity
chirality is how particles get mass - the Higgs field gives fermions mass by coupling their left and right-chiral parts, causing chirality mixing