My take on the elevator-blasting scene in "The Cage":
Pike is kidnapped; sidekicks rush to the site, their weapons at whichever setting. Those who have the stun phaser barrel in place do a quick offscreen adjustment (or then nobody has his gun on stun). Those who have the kill phaser barrel or the laser barrel try their luck with the door. Some are not satisfied with the result and up the ante, either by switching from the general-purpose vaporizing phaser to the dedicated cutting laser (a logical move) or vice versa (a pure frustration move).
And lasers are generally known to be better cutters than phasers, so Tyler mentions the former rather than the latter when telling his superior about the failure... Number One would know that if the laser barrel failed, then the phaser barrels obviously wouldn't have been any good, either.
Two separate barrels for stun and kill in phasers is good, solid canon from STXI. OTOH, multiple barrels of completely different functionality is good, solid canon from ENT, with those plasma rifles that have a separate phase gun overbarrel (as well as from the real world, where assault rifles have separate grenade launcher barrels, or other scifi realms where they have, say, flamethrower barrels!). A three-barrel carousel with two separate phaser barrels and a third barrel for completely different machinery makes good sense, then. Things like power settings or beam width settings are handled by other controls, although the same controls may well apply to all the barrels.
Think of an assault rifle with a grenade launcher and laser sight: three "weapons" that all need triggers (which can be combined, even if today's simple and rugged weapons never try for such a thing) and might be adjusted in things like range (by adjusting a common sighting screw) but definitely need three separate "barrels".
For the actual "The Cage" visuals, the red beams come from the uppermost barrel of a given sidearm. For Spock, that's the longest, stockiest barrel; for Tyler, the carousel is rotated ninety degrees (counterclockwise when viewed from rear) compared to Spock's, so he fires with the slightly shorter and thinner one. Garrison then also fires with the long, thick barrel; and Tyler then twists his gun to bring the long, thick barrel to bear for a second shot, while Spock sees no need to adjust anything. Tyler may also adjust some other knob for his third and final shot, but that'd be offscreen; all we can see is that his barrels have not been rotated a second time.
This could well mean that the shortest, thinnest barrel (the one that Number One has in the firing position when setting her gun to self-destruct) is dedicated to stun. Pike also threatens the Talosian with that one, though - both on the surface, where his training for nonviolence might have taken over, and down in the cave, where he'd have been feeling both the logical need and the self-fanned flames of murderous urge to use a kill barrel. And of course there are cases where no single barrel is in the topmost "firing position"; Pike's carousel often rotates to the two-up, one-down position.
But never mind that level of detail: two phaser barrels and one laser barrel would preserve continuity nicely enough.
Timo Saloniemi