A sump is a seperate body of water, normally hidden from your display tank, where you hide your equipment.
A refugium (aka "refuge") is a seperate body of water, free of any predation, where you can raise beneficial life for your tank. There are all sorts of refugiums. Some go with a deep sand bed refugium to primarily export Nitrate, others grow macro algaes for the same reason, some refugiums target producing pods and other micro foods for the tank, some go with a combination..