The point, as I had understood it, was that if you see ability X, you know for certain that you are fighting a Red Dragon or a Basilisk or whatever. That the abilities conclusively identify the creature, and the creature specifies exactly those abilities. Hence, a 1:1 correspondence. If and only if it has ability X, it is monster A.
That's why Charlaquin said (trimming to the bare necessities) "[P]layers should be able to tell what a monster is (or near enough to the mark) by fighting it, even if the DM doesn’t use its name or describe its appearance beyond minimum necessary detail." In other words, all that you need to know in order to conclusively identify that a creature is definitely a Behir is to see it use its abilities. Some slight leeway is allowed, but the core principle is that a creature should be singularly identified by its abilities. You'd never mistake a flamethrower tank for a red dragon or vice-versa, ever. You'd never conflate, say, a purple worm with a behir, even though both are reptilian beings with bluish-colored scales and some ability to eat people.