Is there a relation between these two distributions ?
I cant say its something that these days the detail is familiar to me, being stuff from the dim past, but the Plank distribution is what you get if the particles are in principle indistinguishable. The Boltzmann-Maxwell distribution is when they are in principle distinguishable.
Interesting thing is I first came on this not in Physics but as an exercise in a Statistical Modelling course.
Couldn't resit refreshing my memory about it - it's on page 148-149 of Ross - Probability Models
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