I don't think they're actually separate in the original lore, so how they differ is really up too you.
Yes, but I'm having trouble thinking of things that would work here, so I'm looking for ideas. That's why I posted this. If I just wanted to come up with something on my own, I wouldn't have bothered.
In general, buying two Sponsored Magics is not very efficient Refresh-wise.
Yeah, that's why I want the two powers to work together. If they have a multiplicative effect, it should be more efficient.
It's true that the full Denarian package isn't either, but you've got to keep in mind that Refresh doesn't exist in-setting. People can't just decide to buy more Refinements because they want them. You've got to take the Powers you can get.
Refresh may not exist in-universe, but free will does. I have no trouble imagining that a wizard is going to have an easier time saying "I'm not going to endanger my free will to gain the ability to turn into a demon-bear! That wouldn't even be all that helpful," than saying "I'm not going to endanger my free will to gain awesome magical abilities which will help me protect myself and those I care about, defeat my enemies, and generally be extremely useful."
The Denarians clearly offer some kind of magic-boosting effect beyond the hellfire one gets from the shadow, because Lasciel's shadow offers it to Harry as a reason to take up the coin to help deal with potential problems with Little Chicago in Proven Guilty.
(As an alternative to a different form of hellfire, I've considered having the Fallen offer some kind of physical immunity to backlash/spell stress, but this doesn't strike me as particularly balanced. Besides which, I'm interested in different types of sponsored magic and like discussing them.)