Gain usually is specified within the context of power output. Often, if no context for power output is given, then this is assumed to be small signal gain. Conditions for small signals at the input and output are usually easy to reproduce and verify, whereas gain and gain flatness can vary significantly when an amplifier approaches compression. Gain flatness for an amplifier with a significant frequency range is often specified over subsets of the entire frequency range, as well as over the entire frequency range.
Gain and Gain Flatness typically include an implicit assumption that the reverse gain from the output to the input is negligible; i.e., the amplifier is unilateral.