All nuclear bombs involve fission. Some (termed "thermonuclear") involve fusion. A fission first stage is detonated to ignite a (much higher yielding) fusion second stage. Most bombs deployed today are thermonuclear simply because it's the most sensible way to scale up the yield of a weapon.
Nitpick, AFAIK (which is t far) the real crust-busters (e.g. Tsar Bomba) use yet a third stage of fissile material that gets rapidly burnt up at truly absurd neutron densities to get that last 40-90 Mt and as a result are dirty as all hell. The Soviets turned that weapon down from 100Mt designed yield to 50 because there was no way to keep it from just radiating everything.
