How does this front shock design work? This is a general question about front shocks in a suspension fork, which I'm just beginning to learn about.  

What kind of shocks are shown in this video, and how do they work?  

In particular:

1) Why are the two sides (left and right) different?  Is that because one is for damping compression, and the other is for damping rebound?

2) Why do the two sides have different diameters, i.e., what's in them?

3) Why do the two sides have a different connector at the bottom?

4) What combination of springs/air/oil is used in each side?
My understanding is that a car has two systems - the springs (leaf or coils) and the shocks/shock absorbers.

Springs absorb the initial impact, but springs alone would be bouncy.  So Shocks (should really be called dampers) are systems which resist change and slow down the spring.

In your bike's fork, one side is a spring and the other is a damper.   They act at different times, and act against each other.

Through axles were invented to help tie both fork legs together so this imbalance would be less of an issue.

In an ideal world you'd have both on both fork legs, but that would mean smaller springs and dampers, which are less effective even when there are two sets.