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Hmm, I thought the units were always cc (volume), but apparently in VOY/ENT, it was mg (mass).
Mass measurements are much more common in medicine than volume measurements in my experience.
I think it is the opposite for something ready to be administered. Sure, a certain mass of the active ingredient is suspended in a specific volume of an inactive medium like saline. But when a physician is ready to administer it, it is much easier to portion out the desired volume of medicine than to weigh it out. As long as the mixture has an established ratio of active ingredient to inactive medium, measuring out the desired volume should be quick and effective.
It could be that the inaprovaline hypospray they use has a ratio of 1mg per 1cc, and that everyone knows that. Meaning that one could say either "20 mg" or "20 cc" and they would be asking for the exact same quantity of the active ingredient.
I'm fresh off 15 years as a paramedic. It kind of depends on the context. If we're pushing a fractional volume of a container (let's say a 10 ml amp of epi 1:10000) then I might say "push 1 ml", because it's the easiest unit to understand in that moment (the amps are marked on the side in MLs). USUALLY, though, I would say/report that I gave 50mg of benadryl or 0.3mg of epi or what have you, because the mass dose of the drug USUALLY matters more than the volume of drug solution (in particular because you can have the same drug available in multiple concentrations or forms).