There are 3 basic types of Squash (& Racketball) Grips: Over grips, Replacement grips and Soft grips.
Soft Grips are by far the most popular grips for Squash and are an "in-between" type of grip and are used either as thicker overgrips or as really thin replacement grips. Most squash players use these to build up their grips slightly or to give extra cushioning, comfort and absorbency. The main brands featuring soft grips are Karakal and Tecnifibre.
Overgrips are literally just those, you put them on top of your existing grip to either save replacing the original grip, or if you sweat a lot during play, so you need something to keep the sweat at bay, or you need a better grip. The only thing you need to watch out for is the different textures. There are "sticky" and "tacky" grips OR "dry" and "towelling" grips, which literally have a texture like blotting paper to absorb the sweat.
Replacement grips are used when your original grip has worn out and you wish to replace it with exactly the same or something very similar.