I present details of the first principle theory of X-ray spectral formation 
in neutron star (NS) and black hole (BH) binaries.  I show this theory 
predicts the spectral index correlation vs mass accretion rate as in the case 
of NS as well in the BH case. In both cases this index correlation is mostly 
correlated to the ratio of energy release in the disk vs that in  transition 
(boundary) layer. In BHs the spectral index should increase and then saturate 
with mass accretion rate because the index as an inverse of Comptonization 
parameter Y and Y-parameter saturates with the high mass accretion in the 
converging flow onto BH. Comparison of this model prediction with X-ray 
observations shows that in BH case the index, indeed, correlates and then 
saturates with mass accretion rate. Moreover this index-mass accretion rate 
correlation allows us to estimate BH masses and distance to the source. 
While in NS sources the observations shows that the index stays the same 
independently of spectral state of the source which can be possible if the 
energy release in the disk is always much smaller of that at NS TL 
(boundary layer).