  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 $\sqrt{s}=200$ GeV at forward and backward
rapidity ($1.2<|\eta|<2.2$). The $\mu\mu$ pairs from $c\bar{c}$, $b\bar{b}$,
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 $c\bar{c}$ and $b\bar{b}$ decays and the pair-$p_T$
distributions are compared to distributions generated using {\sc pythia} and
{\sc powheg} models, which both include next-to-leading order processes. The
measured distributions for pairs from $c\bar{c}$ are consistent with {\sc
pythia} calculations. The $c\bar{c}$ data presents narrower azimuthal
correlations and softer $p_T$ distributions compared to distributions generated
from {\sc powheg}. The $b\bar{b}$ data are well described by both models. The
extrapolated total cross section for bottom production is $3.75{\pm}0.24({\rm
stat}){\pm}^{0.35}_{0.50}({\rm syst}){\pm}0.45({\rm global})$[$\mu$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
two 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.
