The term 'acid western' is an elusive one. First coined by Pauline Kael in her New Yorker review of Alejandro Jodorowsky's El Topo (1970), it wasn't until 2000 and the publication of his monograph on Jim Jarmusch's Dead Man (1995) for the BFI Modern Classics series that critic Jonathan Rosenbaum would expand upon the terminology more specifically.
"What I partly mean by acid westerns," wrote Rosenbaum, "are revisionist westerns in which American history is reinterpreted to make room for peyote visions and related hallucinogenic experiences, LSD trips in particular." He distinguishes these from the "less radical… upheaval of generic norms" that colour "the influence of marijuana on the drifting, nonlinear aspects of the style of McCabe and Mrs Miller (1971)," setting the 'acid western' apart from what he calls the 'pot western'.
I guess it's really a "you know it when you see it" kind of deal.