the S21 is a ratio of energy and not power. So if you are work in a matched world, the answer is yes, they are the same, but if you work in un-matched condition the answer is no, they are not the same.
The S21 measurement is based on a reference impedance, usually 50 ohms. The source and load impedance as seen by the circuit can be changed with LC-transmission line circuits to values that may possibly increase the gain and reduce the noise figure.