These come in three types.

Coil Springs Coil – Springs are what most people are familiar with, and are actually coiled torsion bars 

Torsion Bars – The torsion bar on its own is a bizarre little contraption which gives coiled-spring-like performance based on the twisting properties of a steel bar. It’s used in the suspension of VW Beetles and Karmann Ghias and the rear suspension of Peugeot 205s amongst other cars. Instead of having a coiled spring, the axle is attached to one end of a steel shaft. The other end is slotted into a tube and held there by splines. As the suspension moves, it twists the shaft along it’s length, which in turn provides resistance 

Leaf Spring – Leaf springs are what you would find on most American cars up to about 1985 and almost all heavy duty vehicles. They look like layers of metal connected to the axle. The layers are called leaves, hence leaf-spring . Now image that same shaft but instead of being straight, it’s coiled up. As you press on the top of the coil, you’re actually inducing a twisting in the shaft, all the way down the coil.