That is the funny part. The original SK concept was to have one Rajdhani type of train ( Superfast train with an aggressive schedule) with all classes of travel ( instead of just AC) to Delhil from either the state capital or some important city in the state ( No emphasis on service to state etc. Only emphasis was on end points). It was supposed to be non-stop with only tech halts, but to ensure more coverage, limited halts were added later on. By that definition, KSK via KCG can be called the true SK as it has the most aggressive schedule out of the three.
One thing in IR is that state names are usually given...
more... to trains connecting the state capital to the national capital ( some exceptions are there). It started off that way mainly because at the time of introduction of TN, KK, AP etc, the state capitals were pretty much the only large cities in the states and were naturally the choice of starting point for a train to Delhi and thus these trains were given the state name. While this idea is probably not relevant anymore, the naming convention still continues to this day.