What's the difference between top and side discharge.

Most, if not all, of your sand filters need a vertical (top) discharge, and most, if not all, of your cartridge filters need the horizontal (side) discharge. I'm not sure about DE filters, but I would think they need a vertical (top) discharge as well.

EDIT: Jason is correct; I got tunnel vision and was thinking of the pad packs (pump and filter on a plastic base), because it's what I have. To keep both the pump and filter on the plastic base, I have to have a horizontal discharge pump, because I have approximately 6 inches between the two. If your pump and filter separated, then you could use either.
 
As far as I know it is just a connivence thing. If you are replacing a pump that had the output in a particular place it is often easier to replace it with another pump that has the same configuration. If you don't mind a little plumbing you can use either one you want. Ideally, you want the one that results in a plumbing configuration that has the fewest fittings and the shortest pipe runs. Getting a pump that points a certain way can sometimes help with that. But the efficiency difference is usually very small, almost not worth worrying about.
 
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