  Heavy-flavour hadron production provides information about the transport
properties and microscopic structure of the quark-gluon plasma created in
ultra-relativistic heavy-ion collisions. A measurement of the muons from
semileptonic decays of charm and bottom hadrons produced in Pb+Pb and $pp$
collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV with the
ATLAS detector at the Large Hadron Collider is presented. The Pb+Pb data were
collected in 2015 and 2018 with sampled integrated luminosities of
$208~\mathrm{\mu b}^{-1}$ and $38~\mathrm{\mu b^{-1}}$, respectively, and $pp$
data with a sampled integrated luminosity of $1.17~\mathrm{pb}^{-1}$ were
collected in 2017. Muons from heavy-flavour semileptonic decays are separated
from the light-flavour hadronic background using the momentum imbalance between
the inner detector and muon spectrometer measurements, and muons originating
from charm and bottom decays are further separated via the muon track's
transverse impact parameter. Differential yields in Pb+Pb collisions and
differential cross sections in $pp$ collisions for such muons are measured as a
function of muon transverse momentum from 4 GeV to 30 GeV in the absolute
pseudorapidity interval $|\eta| < 2$. Nuclear modification factors for charm
and bottom muons are presented as a function of muon transverse momentum in
intervals of Pb+Pb collision centrality. The measured nuclear modification
factors quantify a significant suppression of the yields of muons from decays
of charm and bottom hadrons, with stronger effects for muons from charm hadron
decays.
