  The standard model characterizing the GRB spectrum invokes a
four-free-parameters empirical function, so-called the Band model. One
alternative model named cutoff power-law (CPL) implements a power-law plus an
exponential cutoff. These functions obtain almost equally good fits, and are
adopted in nearly all the GRB literature. Here, we reanalyze the sample defined
in Li. (39 bursts including 944 spectra). We classify the spectra by two
methods: (1) checking their corner-corner plots of the posteriors to determine
well-constrained $\beta$ (Band-better) and un-constrained $\beta$ (CPL-better)
categories; and (2) defining four groups by the different of deviance
information criterion (DIC). We found $\alpha=-0.64\pm0.28$ and $\rm
log_{10}(E_{\rm p})=\rm log_{10}(191)\pm0.41$ for the Band-better spectra and
$\alpha=-0.96\pm0.33$ and $\rm log_{10}(E_{\rm p})=\rm log_{10}(249)\pm0.40$
for the CPL-better spectra. With the "Correct" model (the "better" one between
Band and CPL) and v.v. the "Misused" model defined, we find significant
deviations in parameter distributions and parameter relations for the
Band-"Correct" and CPL-"Misused" cases. This means if a spectrum is
best-described as Band, applying CPL to derive the spectral parameters will
prominently deviate from their intrinsic shape, therefore affecting the
physical interpretation. Our analysis indicates that the "better" model should
be duly examined during GRB spectral analysis. In addition, the $\beta$
distribution exhibits a bimodal structure containing Band-better and CPL-better
spectra respectively, inferring Band and CPL both have physical origins.
