cannabineer
Ursus marijanus
rather than edit, i'll say that I did much of my reading here, fun siteHydrogen bombs are a subset of nuclear devices, but the language convention has been nuclear = atomic i.e. pure or mostly* fission devices.
The key term is "thermonuclear", which is specific to fusion reactions. The standard fission bomb is "nuclear" since the reaction is not sensitive to temperature. Fusion reactions only run at high temperatures and pressures, and in practice a nuclear (atomic, fission) first stage is needed to get temp and press high enough.
The yield difference is essentially an artifact ... pure fission devices are limited to about a megaton (ref. Ivy King test) while thermonuclear can be scaled up almost without limit. (ref. Tsar Bomba)
*mostly because modern nuclear bombs are often "boosted" by injecting tritium, which adds "thermonuclear smolder" neutrons to the mix, boosting fissile conversion efficiencies. I read about bomb designs some 20 years ago; fascinating stuff
http://nuclearweaponarchive.org/