Difference between slow, medium, fast AGC
I don't believe there is much more to it than that, especially noting that you are aware not to track so fast that you track out amplitude information for modulated signals where the amplitude is used as part of the modulation (so more so for M-QAM than M-PSK). You can also design AGC's with different rise/fall times so can have "fast-attack" and "slow-decay" for example. 

A reason you may want to have a dynamic AGC is distinguishing operation between acquisition and tracking. During acquisition it would be likely to use a much faster AGC at the expense of noise performance for the benefit of acquiring the signal faster. Then once acquired the loops (AGC, carrier tracking, symbol tracking) can run slower at the benefit of better noise performance but fast enough to track all expected dynamics.