Depending on where you are regionally located in the US, can these
terms be used just about interchangeably in the sense "a hired hand (a
cowhand) who tends cattle and performs many of his duties on
Basically, yes. Of course, like many regional terms, additional associations may be held from region to region, sometimes changing drastically. In my experience, "cowboy" is the most general of the terms in English-speaking parts of the US. "Vaquero" (derived from the Spanish "vaca" for cow) and "caballero" (derived from the Spanish "caballo" for horse) are more commonly encountered in the US in places with a greater Spanish-speaking population. (Side note: the term "buckaroo" is an Anglicized spelling of the Spanish pronunciation of "vaquero.")
In addition, can any of these terms be used interchangeably to refer
to cowboys in western movies? Or to historical cowboys and gunslingers
back in the old days when people had to rely on horses to carry them?
Not really; the terms all refer to people who handle and drive cattle. Just because people rode horses in the "Old West" didn't make them a cowboy, just like riding a horse in medieval Europe didn't make made a person a knight. In short, not only cowboys rode horses. To wit: cavalrymen and pony express riders. Nor were cows the only things that people herded from horseback in the Old West.