Re: Pony up.
Here it's called a live axle. The driveshafts and differential are all enclosed in a chunk of steel, wallowing in hypoid gear oil. These things are attached to the car with leaf springs. This system is simple, strong and cheap, and it keeps both rear wheels vertical when cornering. Cf mark I Ford Escort. But it has various disadvantages. The ride is crap because of the large unsprung weight. The traction is crap because the prop shaft imparts a torque onto the axle which pushes one wheel into the tarmac (good) but lifts the other off the road (bad). That's the single black line from the Mustang in the clip. It's also got terrible axle tramp, where the wheels shake up and down, because the shock absorbers' damping settings have to be a compromise between comfort and performance. Also, you can get bump steer where a bump under one wheel lifts the whole axle which can reduce traction on the other wheel and even twist the axle's steering direction. Oh, and axle wrap, that's no good either!
As Colin Chapman would've told you, you wanna bolt the rear diff to the chassis, move the brakes to the inboard end of the driveshafts, and use wishbones to suspend the axles. He might even suggest using the driveshaft as part of the lower suspension, https://en.wikipedia.org/wiki/Chapman_strut . But he wouldn't tell you that at Le Mans, because the bastards wouldn't let him race.