When the Hulk claps it appears to generate enough force to send people flying. How does this work - is it wind due to the air being pushed out from between his hands, a sonic boom from the sound of the hands meeting, or something else entirely?
It's the same thing that's so destructive with bombs and other explosions at close range, even without shrapnel. In effect, it causes a concussive wave (also called a shock wave).
A shock wave (also called shock front or simply "shock") is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium (solid, liquid, gas or plasma) or in some cases in the absence of a material medium, through a field such as the electromagnetic field. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium.1 Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow. In supersonic flows, expansion is achieved through an expansion fan. A shock wave travels through most media at a higher speed than an ordinary wave.
A sonic boom is another form of concussive wave, so yes, they are similar.
It's a different phenomena than wind, which involves a more steady movement of air.
A better analogy might be a comparison of a wave in the water to the flow of a stream. With a wave, the medium through which it travels doesn't move much. It's a bit easier to visualize the difference (at least for me.)
This article describes how waves work.