A rancher, in the sense that seems to be sought here, is a cattleman, and raises cattle.

The guys (mostly) he hires to take care of his herd are cowboys, and they herd cattle but they rope cows.

The distinction is in the implication of ownership, where "cattle" derives from an old word (catel) related to personal property or capital wealth. If speaking of the herd as the property of the cattleman he's working for, most cowboys would refer to cattle; but if speaking of individual animals or small groups of them, they're just cows. As used by working cowboys, it is an informal appelation that carries NO meaning of gender.

There are specific names that are used when gender or other "characteristics" of a specific "cow" is intended. Heifers, steers, bulls, dogies, etc; but the usage - for at least the last century in cattle country - has been that a cow is any bovine with horns (even if cropped) and a contrary nature.

While there is nothing disparaging or derogatory about herding cows, most old-line cowboys would be offended if you said they raise cows. You raise cattle, and you herd cows. One who "raises cows" is a "A@%#$ farmer" - who probably milks the $#%@! things everyday. It's said with a different inflection, and "it ain't friendly." Or wasn't until the rancher's kids went off to college and got "polited up" recently.

The term "kine" is so archaic that, while most cattlemen probably saw it in a schoolbook, it is never heard. It should be noted that it is a plural and there's no singular still found even in schoolbooks brought in from "back East."

"Ox" and "Oxen" refer specifically to draft animals. They usually refer to animals bred specifically for draft use, but can be used to refer to any animal so used. Cowboys usually know what they are, but they're ain't any around in most parts where you'll find working cowboys - at least since the covered wagons got unhitched (and the farmers who raise cows got tractors).

Cowboys have a number of other "slang" uses for the word "cow," but they are all derogatory and mostly offensive.

John