How does the nuclear reaction generate the destructive shockwave that can be seen? If it just creates "energy" how does that translate into a shockwave?
A modern nuclear warhead, if it's not a "dial-a-yield" model, consumes basically all of its nuclear fuel within approximately one microsecond. During that microsecond, it emits however many kilotons or megatons of energy, mostly as high-energy photons.
The usual way to use a nuclear weapon is to explode it in the air above the target. Most of the photons emitted by the device will be absorbed by a huge volume of air, creating the incandescent "fireball" that you've seen in films.
Raising the temperature of air also raises its pressure. Within a microsecond, the pressure of that huge volume of air is raised high enough to flatten pretty much any above ground structure that wasn't vaporized by the direct radiation. It's the expansion of the heated air that drives the shock wave and the subsequent blast.
And how does that relate to chemical explosions?
"Explosion" usually just means that something flew to bits. "Detonation" and "Deflagration" are terms of art in chemistry that name specific ways of flying to bits. In a detonation, the reaction front moves through the fuel as a shock wave. In a deflagration, the reaction propagates by heat.
There is a chemical detonation that occurs when triggering a nuclear warhead, but if the physicists call the nuclear process "detonation", that's something I would not know about.