Three ways to count

Drag the temperature to the hot end and the three curves sit right on top of each other, close enough that you'd think there was only one. Drag it cold and they come apart into shapes that look like they belong to different problems: a huge spike on the lowest level with nothing anywhere else, a flat shelf that drops off a cliff, and a smooth slide down from the left.

The only thing that differs is a rule about sharing. Bosons (Bose-Einstein, the spike) are happy to pile into the same state, as many as you like. Fermions (Fermi-Dirac, the cliff) can't share at all, so they fill the levels one at a time from the bottom, like seats in a theater. Classical particles (Maxwell-Boltzmann, the smooth slide) don't care either way. When it's hot there's so much room that nobody is competing for a state and the rule stops mattering; the cold end is where it shows.