Actually a Hydrogen bomb is an Atom bomb, or using the correct name Atomic Fusion. It uses Fission (see Atomic) reactions to initiate a Fusion reaction, so far there are no nuclear weapons that use only Fusion.
Also I'm confused AK, are you trying to say that the term Nuclear Weapon apliies only to Hydrogen bombs, it applies to all weapons using Nuclear reactions, be they A bombs (Fission) or A=>H Bombs (Fission to Fusion).