After the selection of LOR as the moon-landing mode, MSFC re-oriented the Nova project to larger launchers of about a million pounds payload to LEO, for Mars missions and lunar base development, and renamed the effort Post-Saturn. MM and General Dynamics were the contractors for the main effort, with Douglas and Boeing having a secondary role.
Class I types were extrapolations of Saturn -- two stages with F-1A and M-1 propulsion, or solid first stages with M-1 upper stages.
Class II introduced recoverable stages and an greater variety of propulsion options, such as plug nozzles and high-pressure hydrogen engines.
Class III was primarily comprised of single-stage designs, fully recoverable, with more advanced propulsion such as air augmentation (as showin in the Renova/R10R-2 option in the "MM Advanced Designs" pic). The conical Martin jobs were the S10 single stage versions, S10E (expendable) and S10R (recoverable).
Class IV was very advanced, often with integrated chemical and nuclear propulsion (such as GD's Nexus).
Boeing continued to develop the solid-boosted Nova concept after the end of the post-Saturn project, first showing a single-stage hydrogen vehicle with massive solid boosters in 1965, and refining that concept into AMLLV in 1967-68, with a range of solid and liquid boosters coupled to a hydrogen core.
Douglas developed OOST and ROOST single stage boosters, which eventually led to ROMBUS and ICARUS.
The basic elements of the Class I post-Saturn systems briefly re-appeared in the SEI era, with Lockheed's review of the "Case 4" in-line tandem-staged launchers with re-born F-1A or M-1 propulsion.