Fermions and Bosons are just a different division. The distinction between the two was discovered prior to the discovery of any of the quarks. More specifically,

Fermions: Any particle that has a spin that is a non-zero integer multiple of one half (+/- 1/2, +/- 3/2, etc.) Electrons, protons, and neutrons are Fermions each possessing a spin of 1/2. Also, a helium 3 nucleus is a Fermion, albeit a composite one (2 protons + 1 neutron), having a spin of either +/- 1/2 or +/- 3/2 depending on its energy state.

Bosons: Any particle that has an integer spin (including zero). All of the force mediating particles have integral spins. The most familiar is the photon, which mediates the electromagnetic force, and it has a spin of 1. The graviton, gravity’s force particle, is theorized to be spin 2. Additionally, you can have composite Boson’s, such as helium 4 (2 protons and 2 neutrons). This has a spin of either 0, +/- 1, or +/- 2, again depending on its energy state.