The particle-physics term fermion refers to a particle
with half-integer spin, i.e., 1/2 different than some integer
(1/2, 3/2, -1/2, etc.).
The particle-physics term boson refers to a particle
with full-integer spin (1, 2, 3, etc.).
An elementary fermion is one that is an elementary particle,
and a composite fermion is one that is a composite particle
(formed of multiple elementary particles whose spins sum to a
half-integer number),
these two categories sharing the characteristics
associated with half-integer spin, including
adherence to Fermi-Dirac statistics.
Example elementary fermions include any of the
quarks and leptons.
Baryons are a class of composite fermions.
Electrons, protons, and neutrons are fermions.
Atomic nuclei are composite fermions if their mass number is odd.
(Nuclei with even mass numbers are composite bosons).