I just don't like "fly." Pet peeve. The other complication is that I add my "continuous" sparge in 2 or 3 "batches," not a continuous flow, so I used to call
that batch sparging... Really the only distinction is between 1) draining completely and reflooding the mash, or 2) adding water while you're draining. And there are so many variations of both. (As for my inner pedant, if I'm not mistaken, the term "sparge" was introduced in 18th century Britain to mean the radical, new idea of using rinse water, by any means, in a single wort, rather than the old methods that either just drained the tun, leaving lots of extract behind, or re-mashed the grains.) So if by "batch sparge" we mean all the drain and refill variants, everything where you add water on top while you drain from the bottom needs a collective name, and I don't think "fly" or "continuous" really captures it. (Know what I kinda like? Courtesy of Buffalo Bill Owens, "slip 'n' slide!" Ok maybe fly is no worse....
)
And Jim, my preference for, um, fly sparging is because I only have to vorlauf once, so the diminishing rate of return doesn't bother me. It's the simplest option given that my tun volume precludes no-sparge. As for that rate of return.... In the end I guess it's all X amount of water passing through Y of grain, and the mechanical details are trivial, as is what you call it. "Fly" might grow on me.