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.

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.

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...