Having heard a fair sample of all three, in general I would say yes, each group tends to have some similar sonic characteristics as a group that will still vary somewhat in comparison case by case.
Class A is more towards a warmer tube amp sound than A/B. Sound is still more damped however.
Class D also is more towards tube amp sound in the sense of being more liquid in the midrange in particular. Sound is very highly damped but more holographic and neutral to colder sounding in particular than most Class A/B.
Class A/B can vary widely all over the place but tends to be more towards the middle of the others sonic traits in general.
Class A is more towards a warmer tube amp sound than A/B. Sound is still more damped however.
Class D also is more towards tube amp sound in the sense of being more liquid in the midrange in particular. Sound is very highly damped but more holographic and neutral to colder sounding in particular than most Class A/B.
Class A/B can vary widely all over the place but tends to be more towards the middle of the others sonic traits in general.