From the introduction to Flashing Swords! (1973) an anthology of original Swords & Sorcery novelettes, edited by Carter:
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?