The gain of a microwave component is a function of the generator and load impedance. There are a number of specific gains that are of special interest to RF / microwave engineers.

Associated Gain (G_A)
The tuned gain of a device when it is matched on the input for optimum noise figure and matched on the output for minimum reflection.
GA = { (1-|opt|^2)|S21|^2} / {|(1-S11opt)|^2}

Maximum Available Gain (G_max or MAG)
The tuned gain of an unconditionally stable device when it is matched for minimal reflection (conjugately matched) at both the input and the output.
Gmax = |S21/S12| (k - SQR[k^2-1])

Maximum Stable Gain (G_ms or MSG)
The gain that would be achieved if a conditionally stable device were first terminated with resistors to the point that it was unconditionally stable, and then conjugately matched at both the input and the output.
Gms = |S21| / |S12|

Power gain (G_P)
The tuned gain of a device when the output is presented with the appropriate loadline L to produce some specified output power, and the input is matched for minimal reflection.
GP = {(|S21|^2) (1-|L|^2)} / {|1-S22L|^2}

Small signal gain (G_ss, or loosely, "Gain")
The gain measured with an amplifier operating in the linear region, and with source and load impedances of 50 ohms. Small signal gain is normally measured a minimum of 10 dB below the 1 dB gain compression point.

Transducer power gain (G_T)
The unmatched gain in a 50 ohm system. It corresponds to the S-parameter S21, and can be calculated from
GT = |S21|^2.

Unilateral power gain (U)
The gain that would be achieved if the transistor were "unilateralized" (feedback set to zero) and conjugately matched.
U = {1/2|S21/S12 - 1|^2}/ {k |S21/S12| - Re(S21/S12)}