A quick review of the code revealed the following:
"analyze distribution" yields the probability of finding a particle of type_b at a certain distance around a particle of type_a. It does so disregarding the fact that a bin for a larger radius represents more volume. Ergo \sum_i bin[i] = 1.
"analyze rdf" calculates the same values for the bins but then divides by (bin_volume / simulation_volume), where bin_volume=(4.0/3.0)*pi*(r_out^3 - r_in^3), so a spherical shell. As far as I see it, this definition coincides with the definition of "the" rdf (
https://en.wikipedia.org/wiki/Radial_distribution_function)
I agree that this is not properly reflected in the User's guide.