The particle-physics term boson refers to a particle
with full-integer spin (1, 2, 3, etc.).
In contrast, a fermion is a particle
with half-integer spin, i.e., 1/2 different than some integer
(1/2, 3/2, -1/2, etc.).
An elementary boson is one that is an elementary particle,
and a composite boson is one that is a composite particle
(comprising elementary particles whose spins sum to an integer),
these two categories sharing the characteristics
associated with full-integer spin, including
adherence to Bose-Einstein statistics.
Example elementary bosons are photons, gluons,
weak bosons (W bosons and Z bosons), and Higgs bosons.
Among the composite bosons are mesons, alpha particles,
deuterium nuclei, and any (other) atomic nucleus with an
even mass number.
Note that some elementary bosons have no (rest) mass and are
always moving at the speed of light (c), while others have mass and
always move at speeds less than c.