First was the gathering and bringing in. For the most part it wasn't done on horseback. It was more apt to be done with a pickup load of feed for bait and a few strategically placed people on foot or horseback (this was pre-four-wheelers) to block escape routes. The truck driver needed a strong voice to call 'em in; every caller I ever knew had his or her own style but the trick is that the cattle have to know it means feed.
Then once they were in the lot, you relied on gates and fences, plus a little more voice work and some instinct for thinking like a cow. Some of the voice work was calling, but more of it was encouraging the herd to move ahead of you. Stockmen I have seen vary on whether they use voice or not. Some don't like the voice cause it riles up the herd. But I always figured a little use at the appropriate time helped, just so you didn't over do it. And if the herd knew the voice was a plus. Some talking to 'em seemed to get them a little familiar with you and somewhat accepting.
Working cattle on foot works if the herd is used to seeing men on foot. I've seen cattle shipped in from the open range that had never seen a man off a horse, and they went plumb loco at the sight. Kind of like sending a country boy to the big city - its a scary experience.
Styles of sorting cattle vary but I always preferred to work with one other person that was used to working with me. The two of us with an easy going dog (not a specially trained one) could do more with a little patience and some good body English than a whole raft of cowboys on horseback. Not that we didn't have use for those cowboys on occasion. For instance if a wily critter went to a neighbor's pasture, especially if it was a young bull, hiring a good cowboy on a good horse was worth it. But for the most part, our horses were more for our pleasure than for stirring up the herd. Course, that couldn't have anything to do with our cowboyin' abilities, could it?
Might change for the next generation: my 9-yr-old grandson has taken up roping in junior rodeo. Now when his dad has a sick calf in the pen that he can't catch, he goes and finds son to come rope it for him. Way to go, Brody!
Even so, one of my favorite stock paper cartoons was of 2 fellas watching a pot-bellied old codger with a bag of feed on his shoulder leading some cattle across the pens. The caption: Joe can do more with a 50 pound bag of feed than 6 cowboys on horseback.
Yes, there's more than one way to work cattle and I suppose whatever fits your situation is the right way. Right?