Fermi–Dirac Statistics describe particle distribution in systems comprising many identical particles that all obey the Pauli exclusion principle. Essentially this means that Fermi–Dirac statistics explain the laws that govern how fermions behave when in large groups (remember all particles that ‘obey the Pauli exclusion principle’ have half-integer spin and are therefore fermions).
Bose-Einstein Statistics describe particle distribution in systems comprising many identical particles that do not obey the Pauli exclusion principle. Essentially this means that Bose-Einstein statistics explain the laws that govern how bosons behave when in large groups (remember all particles that do not ‘obey the Pauli exclusion principle’ have integer spin and are therefore bosons).
The Pauli Exclusion Principle
The Pauli Exclusion Principle states that no two identical particles with half-integer spin (fermions) can occupy the same quantum state simultaneously.
Spin
The spin of a particle is its intrinsic angular momentum– the contribution to the total angular momentum, which is not due to the orbital motion of the particle– In other words, the spin of a particle determines how that particle affects the momentum when it is part of a system of many particles.