The "bump" in the middle of the axles in the photo is the differential housing - the ring & pinion gears and the differential assembly (which allows the wheels to turn at different speeds when you turn a corner) are inside that housing, with solid axle shafts going out to the wheels inside the tubes that also carry the spring and shock mounts. The inner workings of a differential are explained at
www.howthingswork.com (it's easier to understand it when you see it in a diagram than to explain it in words).
The IRS system (on Corvettes and almost all other cars these days) allows each rear wheel to move up and down independent of the other rear wheel, as the two wheels aren't connected together; the differential (on rear-drive cars, not used in the rear on front-drive cars) is solidly mounted to the frame, and is connected to each rear wheel by the half-shafts, which have joints at each end to allow the wheels to move up and down independently of the wheel on the other side while the differential is fixed.
The conventional solid axle assemblies shown in the photo (most commonly seen these days on trucks) are one large single member consisting of the differential, solid drive axles, and wheels, all in one piece; when one wheel moves, the entire assembly moves.
All cars, regardless of suspension design, have shock absorbers; they hydraulically dampen suspension motion to keep the tires in contact with the road surface; without shocks, the springs would just keep "bouncing" the wheels up and down (and would let the body bounce up and down on the springs) after they hit a bump.
