My favorite take on the whole "ion" thing combines the canon facts with Dave Stern's Daedalus
novels and their failed Cascade Ion Drive.
The ion thing refers explicitly to power generation in the context of the Class F shuttle in "The Menagerie" and of the polaric ion power plant of "Time and Again". The VOY episode establishes that it's a risky method, at least in large-scale applications, risky enough that even Romulans agree not to dabble in it! Scotty would thus be duly impressed with a starship powered by a polaric ion reactor without any overt signs of blowing up.
OTOH, shuttles do have antimatter aboard, as part of the power generation and application process - as per the expected flotsam in "Metamorphosis". But do shuttles have tanks of antimatter fuel for power generation, or is antimatter just an intermediate product? Well, runabouts definitely have port and starboard antimatter fuel tanks ("Timescape") in addition to an antimatter pod, singular ("Battle Lines"), which is a bit confusing, but even TNG-era shuttles manage to go without onscreen mention of onboard antimatter fuel.
Still, antimatter as an intermediate is something Starfleet engineers would probably want to do without, as it requires containment fields and dilithium to handle. OTOH, antimatter as your primary means of storing energy is wonderful, as it's the most efficient of those known to real-world science. So all things considered, I'd still like to believe in antimatter as the fundamental power source and fuel of shuttles, at least those designed to go to warp.
So, power from antimatter... But how? In big starships, dilithium somehow mediates (at least after it's properly energized). In small ones, it might be that a less "flashy" technology is in use, both because Starfleet once couldn't spare any dilithium for the tens of thousands of midget craft, and because more "gradual" technologies are safer for craft that can't afford to carry tons upon tons of safety precautions and maintenance personnel.
I'm thinking of how chlorophyll "defuses" the mighty energies of incoming photons by cascading them down chemical cataracts in tiny, harmless fractions of supposed energy quanta. The Cascade Ion Drive might be a means of turning antimatter into power by similar means, in a series of small steps. Make too big a step, though, and everything will go mushroom-shaped pretty quickly. So powering shuttles with CID is fine, but starships require dilithium, unless you want weapons of mass destruction - and even the Romulans signed up on not having those, probably because cascades are more difficult to deal with than simple quanta.
So... "Ion propulsion" in "Spock's Brain" is just verbal shorthand for "ion engine power", as in "The Menagerie", this in turn being shorthand for "ion cascade -mediated antimatter power for engines" as opposed to "dilithium-mediated antimatter power for engines".
(With a cascade system like that, you can probably also join the party at various levels of the cascade, rather than merely at the very top. Say, you can hook up hand phaser batteries to the main engine when your sublight engine quits on you, and run the mains for takeoff, at least for a brief while.)