Good question, To me a running catch dog is a dog that can run a HOT track and /or run on sight. It will catch and hold a hog on its own with correct style and not get cut to ribbons on every hog it catches. It can handle a good sized hog by its self and a pair can hold about any hog. This would be an Australian style finder/ holder.
I do not consider rough curs, or bull dog crosses to be running catch dogs, although many do preform very well at the task, most don't hold clean enough for me.
I personally believe that super rough curs and bulldog crosses that are run with a pack cause more trouble than they are worth. If you are having trouble holding a bay the answer is to breed better quality BAY DOGS.
I believe that the Australian style cross bred dogs and some Dogo's are true running catch dogs and they can be hunted in a way that uses that style to your advantage. One or two or three finder/holder type dogs will catch a lot of hogs and not get cut down every hunt. This type of style when combined with GPS tracking while hunting from 4 wheelers or horses/mules is the future of depredation hunting in my part of the country.
This type of dog can also be used as a long range turn out catch dog or led in to the bay as well. Clean holding style is the difference to me, that is the big difference in the dogs that are bulldogs, or crosses that you can leave down, or will follow horseback. I know that there are many types of dogs that can be used successfully and are being used successfully as RCD's in this way and I in no way think there is anything wrong with doing so if it is working for YOU, because that's all that matters.
I don't really understand using a mixed pack of bay and RCD's because of the safety issue, bay dogs running a track some distance and the RCD's catching along ways off and getting dogs hurt. I have run these type of RCD's but I run "just" them ,no bay dogs, 2 or 3 at a time and they stay short range and catch what they find.
That's just my opinion, I don't care what anyone else does and am not trying to say anyway is better than the other. This was just for discussion sake.
110% AGREE