Charan asked:

“

what is the difference between a atomic and a nuclear bomb?

”

Answer:

Any bomb depending on nuclear reactions for its operation is a nuclear bomb.

Atom Bomb depends on Nuclear fusion reactions (Uncontrolled Chain reaction)

Hydrogen Bomb is a nuclear fusion Bomb, and requires an atom bomb explosion first to generate the necessary temperature for it to start working.

Both Atom Bomb and Hydrogen Bomb are nuclear bombs.