There are multiple kinds of filters, so it's hard to be sure about your exact plumbing. It is common to have a pump before the filter with a gravity return, though, particularly if the filter is not sealed.
If you have multiple media pads in your filter, the first ones will remove some particulates, but the later ones are primarily to provide surface area for bacterial activity to turn harmful ammonia (from fish waste, uneaten food, and decaying material in the pond) into less harmful nitrates (via nitrites, but that's more chemistry than it sounds like you're looking for).
On my front pond, similar in size to yours, I have a pre-filter on the intake to my pump to keep it from clogging. It then pumps out to a filter box with coarse, medium, and fine filter pads. Only the first ones are for particulate removal (and I have a clean-out drain that helps clear out whatever is trapped in front of it). The rest is strictly biological filtration to detoxify the ammonia. I have to clean out the filter pads periodically, but not all at once, so that I don't shut down the bacterial filtration.
