So, as I read it above and in the Wiki, I gather that driveway is a subset of service road? (Actually, in my specific case, it's a little more complicated in that the access to a couple houses and a couple outbuildings are interconnected so it should probably be tagged 'driveway=pipestem' as well.)

Refinement is probably a better word than subset, because it depends on how the data gets used; if someone makes a map that interprets all highway=service the same way, driveways will look just like all the rest. If they interpret service=driveway in addition to highway=service, then they will look different.