  In this work, we consider the process $e^{+}+e^{-}\rightarrow
b\bar{b}+\slashed{E}_{T}$, at the future electron-positron colliders such as
the International Linear Collider and Compact Linear Collider, to look for the
dark matter (DM) effect and identify its nature at two different center-of-mass
energies $E_{c.m.}=500~\mathrm{GeV}~and~1~\mathrm{TeV}$. For this purpose, we
take two extensions of the standard model, in which the DM could be a real
scalar or a heavy right-handed neutrino (RHN) similar to many models motivated
by neutrino mass. In the latter extension, the charged leptons are coupled to
the RHNs via a lepton flavor violating interaction that involves a charged
singlet scalar. After discussing different constraints, we define a set of
kinematical cuts that suppress the background, and generate different
distributions that are useful in identifying the DM nature. The use of
polarized beams (like the polarization $P(e^{-},e^{+})=\left[+0.8,-0.3\right]$
at the International Linear Collider) makes the signal detection easier and the
DM identification more clear, where the statistical significance gets enhanced
by twice (five times) for scalar (RHN) DM.
