Those are just different kinds of plastics, with different properties altogether. I'm no chemist so I can't give you the details, though I'm sure any good dictionary would help...
(poly)styrene is the kind of plastic used to make plastic models and that's the kind you'll find scratchbuilders using. It's normaly coloured and react to 'norma' plastic glues, which basicaly soften and melt the plastic. Scratchbuilders will be more familiar with white sheets of styrene, sold in hobby shops, or plastic manufacturers (way cheaper option!), and used by companies such as Evergreen to produce strips, rods, T-beam sections and all that.
Acrylic is normally transparent, and will not react to normal plastic glues at all. Again, this can be used by scratchbuilders (superglue or epoxy is then required) in sheets or blocks. Acrylic is much harder to work with but scatches easily too.
Expended polystyrene is the kind of light white material that you find in many boxes to keep the goods from being moved, damaged,... Other than for building ground layers on a diorama, or as containers for transporting/keeping your models, there's not much else you can do, modeling-wise with this material...