  It is sometimes stated in the literature that the quantum anomaly is regarded
as an example of the geometric phase. Though there is some superficial
similarity between these two notions, we here show that the differences bewteen
these two notions are more profound and fundamental. As an explicit example, we
analyze in detail a quantum mechanical model proposed by M. Stone, which is
supposed to show the above connection. We show that the geometric term in the
model, which is topologically trivial for any finite time interval $T$,
corresponds to the so-called ``normal naive term'' in field theory and has
nothing to do with the anomaly-induced Wess-Zumino term. In the fundamental
level, the difference between the two notions is stated as follows: The
topology of gauge fields leads to level crossing in the fermionic sector in the
case of chiral anomaly and the {\em failure} of the adiabatic approximation is
essential in the analysis, whereas the (potential) level crossing in the matter
sector leads to the topology of the Berry phase only when the precise adiabatic
approximation holds.
