I suspect the main distinction in weapons designs is whether staging is used or not. Single stage designs will use some fusion through boosting and multi stage designs have multiple fission and fusion components (primary fission boosted with fusion and the secondary has a fission "spark-plug", the main fusion fuel mass and surrounding mass of fissionable material acting as a tamper and the main source of energy).

Most of the energy from most "H-bomb" designs actually comes from fission.