I was once stopped by "shepherds" in OR moving the flock somewhere using a state highway. They looked like cowboys riding their horses. We had to stop while the flock flowed around the car and then the road was slippery for a few miles ;-).
Here's the subtle difference: "shepherds," aka sheepherders, herd sheep. They mainly use dogs to keep the sheep bunched-up.
Cowboys herd cows. They ride some of the smartest and best-trained horses in existence that are adept at keeping the cows where the wranglers want them to be.
Cowboys and sheepherders don't think much of each other because sheep leave the range in very poor condition for cattle. There were range wars back in the 19th century when sheepmen encroached on cattle country. Those antagonistic feelings persist today.
The fact the Hollywood people don't understand that distinction illustrates their ignorance, arrogance and propaganda motives.