It is not completely clear what the quote from the Wikipedia page (October, 2020) mentioned by OP refers to.
Bosons and fermions are by definition1 physical particles that follow Bose-Einstein and Fermi-Dirac statistics, respectively, but e.g. Faddeev-Popov (FP) ghosts (and many auxiliary fields in the BRST formulation) are not physical fields, and therefore not bosons or fermions. Instead they first and foremost carry Grassmann-parity, although they (in the Hamiltonian formulation) often satisfy a CCR/CAR.
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1 In supermathematics, which deals with supernumbers, it is common to refer to Grassmann-even and Grassmann-odd variables as bosons and fermions, respectively, but it is strictly speaking a misnomer.
This post imported from StackExchange Physics at 2020-12-12 20:04 (UTC), posted by SE-user Qmechanic