For "Analog AGC" we use analog control components (typically voltage variable amplifiers and voltage variable attenuators) to adjust the receiver gain, and we use an analog power detector to measure the total band power (within the bandwidth of the filtering up to the detector). This measured power is compared to a target which generates an error signal (often with an op-amp in an analog circuit) and the error is integrated in a loop filter (also often with the same op-amp) which then integrates to the control voltage needed to make the error go to zero (and the loop filter can be further modified for higher order loop control). In the end the band power AS MEASURED AT THE DETECTOR will be constant except for dynamic conditions during power transitions. Depending on what is used in the receiver for gain control, the AGC can amplify or attenuate the all the signals in band as allowed.
Digital AGC is not necessarily the first block after the ADC, or at least the level detector part of the AGC loop. A significant benefit of doing a subsequent AGC digitally is that you can measure the level (which sets the level of the overall waveform within the bandwidth at the detector) after more thorough filtering of the channel signal of interest and rejecting out of band interference (which could include other channels in a multiband receiver). This interference would reduce the signal of interest in band when AGC'd (power measured) earlier in the chain. Consider the above case earlier for the analog AGC where we have a very strong interference signal near the channel bandwidth of interest, so close that filtering in the analog would be costly. Assume too that we have a high dynamic range ADC with excess dynamic range allowing us to shift some of this filtering challenge to the digital. The analog AGC's purpose is to avoid excessive clipping at the ADC input (or other similar level sensitive components in the receiver chain), so with the strong interference our signal of interest will effectively be significantly attenuated, give the interference will set the full scale level at the ADC input.
NoNot quite. Both analog and digital AGC provide a fixed level of channel power, as measured by the relevant power/signal detector used. What may more likely occur in the analog is strong interference controlling the AGC, so the AGC sets its level based on the interference and not our signal of interest. The AGC only measures power and does not recognize signal from interference: we help that with filter design.