An interesting question.
The subtle difference is in the motive. Horses can herd and horses can kill. However the difference is in the motivation.
Horses do not hunt their food. A predator by nature relies on flesh as it's food source. Horses may kill but they do not hunt. They graze.
I think that is a matter of semantics.
A herd of secretaries descend on the lunch buffet to graze on a big veggie plate.
Horses hunting for more nutritious and sustaining grass to fatten for winter.
Horses hunt for shelter.
People that flock together like a herd even though they don't agree with each other.
I don't kill for sport.
Does that make me a prey animal?
We are more alike than many want to consider.
I can spook at a strange shape.
I can go off my feed if I am too hot or cold or in a strange place.
I am relaxed with friends and nervous around strangers that I do not know their intentions.
I don't like being told what to do and like being asked.
My feet are sore without shoes but if I go barefoot for a month or so they toughen up.
Look of the similarities and not the differences.