There are 3 (or maybe 3 and a half?) distributions that we shall look at : Maxwell-Boltzmann distribution, Fermi-Dirac distribution and Bose-Einstein distribution.
Boltzmann distribution concerns distinguishable particles. Its half-cousin is the Maxwell-Boltzmann distribution, which applies to dilute gases. They resemble one another so much that many people don’t even care to make a distinction between them.
Maxwell-Boltzmann statistics simply takes away the N! factor from w, which makes no difference to the partition function and the distribution function. Hence the two distributions are often taken to be the same.
Fermi-Dirac particles are loners – they cannot share the same quantum states with each other, i.e., they obey Pauli’s exclusion principle.
Bose-Einstein particles are social animals, they prefer staying together than being left alone.
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