  Some quasi-thermal (QT) dominated gamma-ray bursts (GRBs) could be well
described by a multi-color blackbody (BB) function or a combined model of BB
plus non-thermal (NT) component. In this analysis, two QT radiation-dominated
bursts with known emission properties (GRB 210610B likely from a hybrid jet,
and GRB 210121A with a spectrum consistent with a non-dissipative photospheric
emission from a pure hot fireball) are used to make a comparison between these
two modelings. To diagnose the magnetization properties of the central engine,
the `top-down' approach proposed by Gao \& Zhang is adopted. It is found that
diagnoses based on these two modelings could provide similar conclusions
qualitatively; however, the modeling with mBB (or mBB+NT) may give more
reasonable physical explanations. This implies that impacts from the GRB jet
structure and the geometrical broadening on the observed spectrum should be
considered. However, conservatively, these methods may be not sensitive enough
to distinguish between the pure hot fireball and a mildly magnetized hybrid
jet. Some other information is necessary to provide more evidence for the
determination of jet properties for similar GRBs. Based on these
considerations, we suggest that the photospheric emission of GRB 221022B is
from a hot jet; a dissipation is caused by a internal shock (IS) mechanism due
to the increasing Lorentz Factor with time, which makes its prompt emission
behaves a typical evolution from thermal to NT.
