PHENIX reports differential cross sections of mu mu pairs from semileptonic heavy-flavor decays and the Drell-Yan production mechanism measured in p + p collisions at root s = 200 GeV at forward and backward rapidity (1.2 < vertical bar eta vertical bar < 2.2). The mu mu pairs from c (c) over bar, b (b) over bar, and Drell-Yan are separated using a template fit to unlike- and like-sign muon pair spectra in mass and p(T). The azimuthal opening angle correlation between the muons from c (c ) over bar and b (b) over bar decays and the pair-p(T) distributions are compared to distributions generated using PYTHIA and POWHEG models, which both include next-to-leading order processes. The measured distributions for pairs from a are consistent with PYTHIA calculations. The c (c) over bar data present narrower azimuthal correlations and softer p(T) distributions compared to distributions generated from POWHEG. The b (b ) over bar data are well described by both models. The extrapolated total cross section for bottom production is 3.75 +/- 0.24(stat) +/-(0.35)(0.50) (syst) +/- 0.45(global) [mu b], which is consistent with previous measurements at the Relativistic Heavy Ion Collider in the same system at the same collision energy and is approximately a factor of 2 higher than the central value calculated with theoretical models. The measured Drell-Yan cross section is in good agreement with next-to-leading-order quantum-chromodynamics calculations.