PHENIX reports differential cross sections of μμ pairs from semileptonic heavy-flavor decays and the Drell-Yan production mechanism measured in p+p collisions at √s=200 GeV at forward and backward rapidity (1.2<|η|<2.2). The μμ pairs from cc¯, bb¯, and Drell-Yan are separated using a template fit to unlike- and like-sign muon pair spectra in mass and pT. The azimuthal opening angle correlation between the muons from cc¯ and bb¯ decays and the pair-pT 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 cc¯ are consistent with pythia calculations. The cc¯ data present narrower azimuthal correlations and softer pT distributions compared to distributions generated from powheg. The bb¯ data are well described by both models. The extrapolated total cross section for bottom production is 3.75±0.24(stat) ±0.500.35(syst)±0.45(global) [μb], 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.