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I think it fair to equate Goetia with Sorcery and Magia with Spells. So I would have to disagree with your suggestion, Boromir. Saruman did not use evil spirits for the explosions, as far as we know; at least, the text of LotR doesn't suggest it in any way.
As for the Mouth of Sauron versus the Witch King, the Rings were all about sorcery as their power resulted in the undeadness of the Ringwraiths. They were not dead but they were not alive in a human physical sense: they were in the negative Ring-world, which seems identifiable with the spirit world. Think of Weathertop and Frodo's 'vision' of Glorfindel as a being of white flame at the ford. So the Mouth of Sauron is 'into' sorcery, for he is apparently using the power of evil spirits to prolong his life far beyond that of his fellow humans; but he, unlike the ringwraiths, is not undead.
Whereas the Mouth is lieutenant of Barad-Dur, the Witch King is 'field marshall', for all practical purposes, of the armies of Mordor, and lieutenant at Minas Morgul; so they are equal in rank, having different kinds of roles. The Mouth's is 'political', whereas the Witchking's is military. Both are slaves of Sauron. Who is more powerful? I'm not sure. The Witchking is single-minded, having no more self-will (though he is self-conscious enough to understand the prophecy about himself), and is therefore a very effective tool. The Mouth is vain and ambitious and a coward for all his dubious control over evil spirits, and still wears his "mortal coils", and for all his power still loves his life, which in a certain sense translates as a weakness and lack of singlemindedness. Will he die for the sake of Sauron if offered his life in exchange for betraying him? One has to wonder.
For me the single-mindedness and ferocious will to do every last thing Sauron wants makes the Witchking seem more powerful to me than the cowardly, obsequious Mouth.
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