Both are saturated zones of rock or soil that yield groundwater. But whether that zone sits open to the surface or is trapped under pressure between impermeable layers decides how a well behaves, how vulnerable the water is to contamination — and whether it needs a pump at all.
An unconfined aquifer has its upper surface — the water table — open directly to the atmosphere through the overlying unsaturated soil. Rain infiltrates straight down from the surface, and the water table rises and falls with recharge, exactly like the water level in an open, unlined hole in the ground. A confined aquifer is sandwiched between two confining layers (aquitards)— impermeable or near-impermeable clay or shale beds — that seal it off from direct vertical infiltration where the well is located. That seal doesn't mean the aquifer is empty of pressure, though: it's recharged somewhere else, often miles away, at a higher elevation where the same formation is exposed at the surface. That elevation difference pressurizes the water trapped below the confining layer, so when a well is drilled through the confining layer into a confined aquifer, water rises in the casing well above the top of the aquifer itself — sometimes all the way above ground level.