  Neutron stars (NSs) and white dwarfs (WDs) are characterized by different
geometric and physical properties, but their observed properties are often
similar, making them difficult to distinguish. Therefore, it is desirable to
search for their spectral features that could be easily identified from
observations. We present spectral and timing signatures of NSs and WDs hosted
in accreting X-ray binaries that can be easily identified from X-ray
observations. We perform spectral and timing analysis of 4U~1636--53 and
SS~Cygni, as typical representatives of such NS and WD binaries, based on their
X-ray observations by RXTE, ASCA, Suzaku and BeppoSAX uising {\it
Comptonization} spectral model. As a result, we formulate a criterion that
makes it easy to distinguish NS from WD in such binaries: NS X-rays exhibits
clear quasi-stable behavior with the index $\Gamma\to2$ and is characterized by
quasi periodic oscillations (QPOs) at $\nu_{QPO} >0.5$~Hz, although WD X-rays
is stable with $\Gamma \to1.85$ and is accompanied by QPOs at
$\nu_{QPO}<0.05$~Hz during source outbursts. In addition, we revealed that in
4U~1636--53 the mHz QPOs anti-correlate with the plasma temperature, $T_e$ of
Compton cloud (or the corona around a NS. This allowed us to associate mHz-QPOs
with the corona dynamics during outburst cycle. The above index effect, now
well established for 4U~1636--53 and SS~Cygni using extensive observations, has
previously been found in other low-mass X-ray NS and WD binaries and agrees
well with the criterion for distinguishing NSs and WDs presented here.
