I'm not sure which variant is "the same regardless of who and why you ask".
By "the same regardless of who and why you ask," I mean something at least as picky as "the same regardless of what algorithm you try to use to distinguish them." Notice that the pickiest equality operator in a language is the only one that can satisfy that description; any pickier one would be an algorithm (well, a black-box algorithm) that acted as a counterexample.
I think 'eqv? is this operator in standard Scheme and 'eq? is this operator in any given Scheme implementation (but I dunno, maybe it's more hackish than that in practice). Meanwhile, I think 'is acts as this operator in a "standard" subset of Arc in which strings are considered immutable. (A destructive algorithm can distinguish nonempty mutable strings.) I avoid string mutation in Arc for exactly this reason.
So the semantics of is are actually quite fungible.
Yeah, especially once you get down to a certain point where nothing but 'is itself would allow you to compare things, then 'is is free to be however picky it wants to be. A minimally picky 'is would solve the halting problem when applied to closures, so something has to give. :)
The least arbitrary choice is to leave out 'is altogether for certain types, like Haskell does, but I dunno, for some reason I'm willing to sacrifice things like string mutation to keep 'is around. I mean, I think it's for the sake of things like cyclic data structures, uninterned symbols, and weak references, but I don't think those things need every type to have 'is.... Interesting. I might be changing my mind on this. ^_^