You guys are agruing over semantics...
Here's the definition of an atom bomb from dictionary.com:
atom bomb
n.
1. An explosive weapon of great destructive power derived from the rapid release of energy in the fission of heavy atomic nuclei, as of uranium 235. Also called A-bomb, atomic bomb, fission bomb.
2. A bomb deriving its destructive power from the release of nuclear energy.
atom bomb
n : a
nuclear weapon in which enormous energy is released by nuclear fission (splitting the nuclei of a heavy element (uranium 235 or plutonium 239))
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nuclear weapon
n.
A device, such as a bomb or warhead, whose great explosive power derives from the release of nuclear energy.
nuclear weapon
n : a weapon whose explosive power derives from a nuclear reaction
nuclear warhead
n : the warhead of a missile designed to deliver an atom bomb
nuke
n.
1. A nuclear device or weapon.
2. A nuclear-powered electric generating plant.
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They're different types of nuclear reactions (Fission or Fusion) but they are still nuclear reations.. Here's a cool site too..
http://www.howstuffworks.com/nuclear-bomb.htm