s21 parameter
S21 is the square of power gain.the ac analysis is the voltage gain.this is the most significant difference between them. In physics ,we have equation of Power=Voltage*current=woltage*voltage/resistance.so only under special input and output impedance the power gain equals the voltage gain.
usualy the S21 is used in RF designs in which the transmitted or received power is more important.the AC gain is used in Analog circuits,the small signal amplifying characteristic is more important.