A "filter" sump is basically a vessel that holds the overflow water from your tank, it is returned via a pump. Some also keep some equipment there like protein skimmers, heaters, others additional live rock. A refugium is a tank set up just for nutrient export,mainly nitrate. It consists of a fairly deep sand bed where micro fauna can live (pod's, brittle stars, bristle worms). It will also contain macro algae to rid the water of nitrates. Because you have algae in it it will require a light source. most use pc lighting since it is cheap and algae doesn't need a high light output. Most run the light cycle of the refugium the opposite from the main tank lighting. When the main tank light is on the refugium light is off and vice versa.
Some others will chime in with a little more detail then i am giving......don't have much time.....going on VACATION!
HTH