Can you compare the atomic bomb to the hydrogen bomb?

Answer 1

Yes, however on one level they are the same thing as both obtain their energy from the release of excess nuclear binding energy. However as the terms have traditionally been used the differences are as follows:

• atomic bomb, a rather simple bomb operating with nuclear fission of heavy element(s) within a "prompt supercritical mass" of a fissile isotope initiated by a pulse of neutrons. The most commonly used fissile isotopes are plutonium-239, uranium-235 (uranium-233 could also be used but has properties similar to plutonium-239). The yield of such a bomb is limited to less than one megaton (with the highest yield such bomb ever tested only half that).
• hydrogen bomb, a rather complicated bomb operating with nuclear fusion of light element(s) compressed and heated using x-rays generated by either an atomic bomb or another hydrogen bomb in a previous "stage" of the bomb. This "staging" principal permits the yield of a hydrogen bomb to be as large as desired, also the yield can be increased (as well as the fallout) by enclosing the bomb in uranium (even the nonfissionable isotope uranium--238 usually considered "waste" after enriching uranium-235 for atomic bombs can be used) which will be fissioned by the high energy fusion neutrons. This can multiply the yield of the bomb by a factor between 2 to 10 times!

However almost all modern nuclear weapons use both fission and fusion to optimize the bomb's size, weight, yield, etc. for the specific military purpose it is intended to be used for. So the lines are quite blurred.

Answer 2

Atomic bombs are fission weapons. Hydrogen bombs use fission/ fusion. Both are Nuclear weapons.