The hogs you are talking about were for the most part still tame hogs, my dad remembers as a boy doing exactly what you are talking about.
They would make hog drives from Barksdale to Uvalde just like a cow dirve.
They were in no way or could in no way be compared to the wild hogs as we know them today. Totally different breed of animal, build different and acted more like a range cow not really wild but just wild enough you couldnt pet one and had to work to pen one. The dogs they used were thier all purpose dogs that did everything from work stock to keep coons out of the corn to baby sit the kids when they were board. The dogs were cur dogs and by that I mean cur in the truest since of the meaning they were crossed up dogs that had a little of this and that in them but would mostly work hogs like cattle because that is the only way they could do anything with them.
The story Ole Yeller is about as real as it gets from Hollywood.
http://www.huttohounds.com/hillcountryhogdrives.htm I didnt write this but you might want to read it, it is a very nice article about the topic.
As for when did catch dogs come into play, not until John Q public found out there was a sport that made you feel like a "HE MAN" for sticking a boar with a knife and only then because men like me and some others were able to keep "John" safer useing a lead in catch type dog, as younger hunters came into the "sport" they just thought a catch dog was needed and as for me I reliezed that the catch dog sure made my life easier even if "John Q" was along or not.