I don't mean different grips per say...but possible different pressure and exactly how you grip the cue.
If you study a lot of the grips of good players they all vary from shot to shot. I don't mean drastically....but depending upon the distance from the cue ball to the object ball, the type of english you wish to apply, the amount of force you intend to use.....the same exact "grip" will not work for every shot.
That is what I mean. I don't mean drastic differences...but there are some.
For example. On power draw shots I really like using just my index and thumb, because I know I'm going to tighten up at the point of impact, yet I want to make sure I don't steer the ball. For me that works.
For a center ball english shot (which is often as possible) or aiming somewhere in that vicinity on the cue ball I will use my index, middle...and sometimes the cue will rest on the third finger. If there is a long stretch...to ensure the cue is level, I might rest the cue just on my middle and third finger....as I have a tendancy to steer with the index on that shot messing up my accuracy.
I could go on and on...but that is what works for me. That is what I mean by different grips. As I said before....it is good to learn solid fundamentals from a qualified teacher. Once you have those down, I think your grip will come rather naturally, but from paying close attention to my own game I will say there are different 'grips' for pool...as in fingers you might use, and positioning on the butt of the cue.
Again, that is just my two cents. I'm no Certified instructor or anything....but I know a thing or two about a thing or two.