We call a story Sword & Sorcery when it is an action tale, derived from the traditions of the pulp magazine adventure story, set in a land, age or world of the author's invention - a milieu in which magic actually works and the gods are real - a story, moreover, which pits a stalwart warrior in direct conflict with the forces of supernatural evil.
Carter goes on to say that, although the term was coined by Fritz Leiber, Robert E. Howard should get credit for founding the genre.
As with all genre generalisations, it is easier to think of exceptions than rules. But given this is from Carter, one of the editors/authors/canonisers at the heart of the movement, it is fair to take this at face value. This is the 'institutional' definition. That is, for what 'Sword & Sorcery' meant at the time. My challenge would be - does this still apply? And, even looking back, can we still apply this definition now to stories written then?
Two things that immediately spring to mind:
First, 'Pulp magazines' are no longer nearly as relevant as they were. Even in the 1960s, they still existed in some format, but, more importantly, the Sword & Sorcery authors grew up reading (and sometimes) writing for them. Now, that's just not true. Magazines - or 'zines of any form - are no longer the (or even 'a') platform with substantial relevance. That said, we now have a generation (or multiple generations) of authors that grew up with other non-book fantasy influences. For example, video games, tabletop roleplaying, television and, of course, movies. It feels mean to say, but I'd argue that Arnold's Conan is probably a bigger influence on modern fantasy writing than Howard's.
Specifically when it comes to Sword & Sorcery, I'm tempted to put video games at the top of the pile. When it comes linear storytelling, a focus on entertainment as primary virtue and decisive characterisation, gaming is where it is at. Richard Morgan, Rebecca Levene, Den Patrick and Joe Abercrombie are several of the many, many S&S-inflected fantasy writers to openly cite video games as an influence on their writing.
Second, 'a stalwart warrior in opposition to [supernatural] evil' is really intriguing. And, this breaks down into three bits:
Second-the-first, given the prevalence of gritty 'realism' and grimdark now, is fantasy still about good versus evil in this same way? Are our warriors stalwart, in the sense of a Good-aligned? Or are they merely stalwart in the sense of courageous? And even that, it is sometimes with palpable reluctance. Does this even apply? Or are we now firmly in the realm of lesser or necessary evils versus greater ones?
Second-the-second, maybe this was never true. As noted in this (very fun) discussion on r/fantasy, period Sword & Sorcery writers like Moorcock explicitly created a Chaos/Order axis to avoid any sort of objective standards of Good/Evil. Conan was a barbarian - deliberately outside of civilisation and its stuffy ethics. Fafhrd and the Gray Mouser are in thrall to mysterious eldritch masters and have certain, um, proclivities that are more than a little dubious.
Second-the-third, maybe this was true then but now now? The standards of literary heroism in 1972 are substantially different than now - as well as the cultural mores around them. In the past 40-odd years, the way we scrutinise and judge our heroes (real and fictional) has changed substantially. Maybe we're now more attuned to problems with race and gender, and having different discussions about ends and means and whatnot. Carter's definition could've be very true then, but if we attempt to apply it now in a strict constructionist way, it falls apart.