What was the important difference between an atom bomb, Hydrogen bomb and nuclear bomb?

See, Hydrogen bomb and atom bomb both fall under the category of Nuclear bomb as they both cause damage with the help of nucleus of the atom. Now, an atom bomb causes destruction with the help of fission when the nuclei get separated from the atom causing a large amount of heat and energy. Hydrogen bomb includes fusion of nuclei... when they collide to form another atom like 4 hydrogen nuclei combine to release 18 MeV of energy. But hydrogen bomb requires too large a temperature(about 1lac degree Celsius). Moreover... to burst one hydrogen bomb.. four atom bombs have to be blasted so that this temperature can be attained and then hydrogen bomb bursts. Hydrogen bomb is way more destructive than an atomic bomb coz it includes fusion rather than fission.