Can someone help me understand what the different types of pistons are used for? I know there are dished, flat-top, and domed. Are these used to achieve different CRs, or more closely match with a combustion chamber type, or what? I know what each piston is looks-wise, but other than that I'm clueless. Thanks.

Setting the CR is the main reason. I've heard that reverse dome pistons ("D" cups) make the best shaped combustion chamber but they normally require a small chamber to get any compression (depending on displacement). Flat tops are next and work extremely well, flame propagation is great. Domes are the worst, the dome gets in the way of the flame travel. A full dish isn't a good idea since the quench area is substantially reduced.