No, you can have a fusion booster, like in the "Sloika" [0] design, but for a Teller-Ulam design, that is a H-bomb, you use a nuclear primer to ignite a fusion reaction and by far the most energy comes from the fusion part. [1]

[0] https://www.atomicarchive.com/history/hydrogen-bomb/page-11....

[1] https://nuclearweaponarchive.org/Library/Teller.html

You are correct that in a Teller-Ulam design most of the energy can come from fusion, but as a note it's generally a fission-fusion-fission design in "modern" deployments with about 50% of the energy coming from fusion.

https://en.wikipedia.org/wiki/Thermonuclear_weapon

Only very large bombs, such as the Tsar Bomba (97% from fusion) ever where primarily fusion, and those are not in modern arsenals.

Half of the energy comes from the fissile "spark plug" that's inside the fusion material. Less than half of the energy comes from fusion.

It still very much is a fission weapon.

You have it backwards. The fission component is just the "trigger" for the fusion element, which produces the vast majority of the energy release.

Half of the energy comes from the fissile "spark plug" that's inside the fusion material. Less than half of the energy comes from fusion.

It still very much is a fission weapon.

Nope...

"thermonuclear bomb, also called hydrogen bomb, or H-bomb, weapon whose enormous explosive power results from an uncontrolled self-sustaining chain reaction in which isotopes of hydrogen combine under extremely high temperatures to form helium in a process known as nuclear fusion."

Yes, but if you get into the details... The second stage of a bomb is the fusion in which a cylinder of hydrogen and/or lithium is encased by U-238. The primary stage, a trinity-like a-bomb, forces the cylinder to compress by its x-rays. The fusion reaction creates a bunch of energy, but more importantly a huge amount of neutrons. These neutrons cause the u-238 to undergo fission, which is responsible for a majority of the energy and pretty much all of the fallout.

The fissile "spark plug" inside the fusion material is responsible for the majority of the energy...