T-rigged= Worm weight sits on top of worm, pegged or not.
C-rigged= weight is suspended above the worm by a swivel. Usually a 2-3 foot leader.
Having the hook exposed has nothing to do with it being T-rigged or C-rigged. In fact, or should I say IMO, you should have the point of the hook barely coming through the worm on T-rig or C-rig. You don't want the hook point fully exposed. If you rig your worm the same way as, for example a fluke, then you want to run the point back into the worm, just under the "skin."
Fishing a worm weightless is neither T-rig or C-rig. It is simply called "weightless."