A sump is just a huge filter that is great for bio filtration utilizing bioballs or some other form of usually synthetic media. However, many people are using live rock in place of their bioballs because bioballs are known to be nitrate factories. Protein skimmers are used in sumps as well as heaters and other equipment. However that is not to say that you couldn't place these in a proper place in a refugium.
A refugium is exactly what it sounds like, a refuge. You can put beat up fish, corals, inverts or whatever in it. In many cases people use them as a type of filtration where they sometimes place plants that take nitrates, phosphates, sulfates, etc. out of the water column. They can also be useful in growing cultures of copepods and other highly beneficial microorganisms. Refugiums almost always require slow water movement (under 400 GPH) and no water agitation.
Nowadays, people are converting sumps into a sort of hybrid refugium. At least that is the case for me. I have a Megaflow model 2 sump and use live rock as bio filter with about 10 lbs of sand in the bottom and have a ton of bristle worms to eat detritus and other wastes. I also have a live rock with caulerpa (saltwater plant known to be a highly effective nitrate reducer) on it in the sump.
Click reply on the top of my post to see my attached picture of my sump.