  The narrowness of the distribution of the peak energy of $\nu F_{\nu}$
spectrum of gamma-ray bursts (GRBs) and the unification of GRB population are
great puzzles yet to be solved. We investigate the two puzzles based on the
global spectral behaviors of different GRB population in the $HR-E_{\rm{p}}$
plane (HR the spectral hardness ratio) with BATSE and HETE-2 observations. It
is found that long GRBs and XRFs observed by HETE-2 seem to follow the same
sequence in the $HR-E_{\rm{p}}$ plane, with the XRFs at the low end of this
sequence. The long and short GRBs observed by BATSE follow significantly
different sequences in the $HR-E_{\rm p}$ plane, with most of the short GRBs
having a larger hardness ratio than the long GRBs at a given $E_{\rm{p}}$.
These results indicate that the global spectral behaviors of the long GRB
sample and the XRF sample are similar, while that of short GRBs is different.
The short GRBs seem to be a unique subclass of GRBs, and they are not the
higher energy extension of the long GRBs (abridged).
