Although "stockman" is used out here in the western U.S., "rancher" is far more common. "Stock grower" also is used at times, especially in the various "Stock Growers Associations." We also have "cattlemen's associations."
In any event, the terms refer to the people who own the animals and the operation.
Oh, my grandma would give somebody a lecture! She was a homesteader in the West, a stockman's wife.
Stockman -- rancher, someone who raises stock (animals, especially cattle)
Herdsman -- not use in AE
Herder -- used in AE. Ex: sheep herder. Herding means moving animals around the territory, without fences. Sheep herding ruined the land for cattle, and there were fights and even a "war" between cattlemen and sheep herders.
My grandmother would have be highly insulted if anybody had referred to her husband as a "herder" or "herdsman" He was a cattleman.
So there is a big difference in AE between stockman and herder. These words might have quite different connotations in British English, however.
In the US also, at least in the northeast, a person in charge of a dairy herd is a herdsman. If you are a female herdsman, as I was 30 years ago, there's no good word for you. Maybe times have changed since then.