A sump is basically just a container that holds water underneath your main tank. It can be as simple as a rubbermaid container, or as fancy as a plexiglass fortress. It can hold your equipment such as pumps, heaters, and skimmers. It can also hold LR
rubble for extra filtration, and anything else really. Dividers (baffles) can direct water flow to separate it into different compartments for the return pump & skimmer, etc. Outflow brings water in, return pump brings water back into your main tank.
A refugium can be part of a sump (if you add dividers in the sump for it), or it can be a container on its own where microalgea is grown to reduce nitrates. Lights are added to keep the algea alive.. this is a highly effective means for filtration. Kinda looks like a mini-forrest if you like to consider it that way... check some of the user images for examples of them.