An elementary particle is a subatomic particle with no further substructure. It is not composed of other particles. Fermions and bosons, are both thought to be fundamental particles.
Fermions: Fermions obey the Pauli exclusion principle (only one fermion can occupy the same quantum state at once) and have a half integer spin. These are the quarks in their six flavors (up, down, charm, strange, top, bottom) and the six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino). A fermion can be an elementary particle, however, it can also be composite, such as the case of the baryon, which is composed of three quarks. Fermions, here, would also include antimatter particles. The name fermion was coined by Paul Dirac and from the physicist Enrico Fermi.
Bosons: Bosons are generally considered to be the force particles. These include the gauge bosons and the scalar Higgs boson. Bosons mediate interactions among fermions. In fact, there are 5 bosons that are elementary:
the scalar Higgs boson
the gauge or vector photon
the gauge or vector W+-
the gauge or vector Z
A particle containing two or more elementary particles is known as a composite particle.
Ordinary matter is composed of atoms. It was once thought that atoms were elementary. In fact, atom, means "unable to cut" in Greek. The existence of the atom was controversial until about 1910. Some of the leading physicists regarded molecules as mathematical illusions. It was thought that matter, ultimately was composed of energy. In the early 1930s, some of the constituents of the atom were discovered: the electron, the proton and the photon. Our notions of particles was also being radically transformed by the quantum theory's notion of wave-particle duality.
Through the quantum theory, the quark content of the proton and neutron was discovered. Remember, that a proton is two up quarks and a down quark, while a neutron is two down quarks and an up quark.
Elementary particles are either fermions or bosons. They are distinguished by their statistics. They either obey Fermi-Dirac statistics or Bose-Einstein statistics. The spin-statistics theorem declares that fermions have a half integer spin, while bosons have an integer value spin.