[William Cloud Hicklin]

GLoB:

I think you're looking at the Machine/Magic issue a bit orthogonally, using "magic creatures" for Elves and Dwarves whereas "machines" means things that operate mechanically with cogs and gears, a primary-world frame of reference.

Think of Machines instead as "devices that harness the laws of physics for material ends"- given that in Tolkien's universe "magic" is one of the laws of physics. Elves and dragons are as natural as horses and men. In a universe so constituted, with what we call "magic" as one of the inherent forces of nature, one can build a tool or machine that uses heat, pressure, leverage, runes, spells, and/or enchantments: ultimately the issue is making a labor-saving device which alters physical reality according to one's desire, whether Grond or a Great Ring.

Magia/goetia is a bit different, since here Tolkien is talking about illusion or vision not actual physical effect. He's trying to distinguish the "deceits of the enemy"- illusions calculated to deceive, such as Sauron's trap for Gorlim - with "faerian drama" which is intended as Art even if thickheaded mortals confuse the effects as "real", and with things like the Mirror of Galadriel or the palantiri which present Truth even if in a confusing manner.

[Even that distinction isn't a bright line; the Dead Marshes could be seen as an exercise in Art according to a dark Sauronian aesthetic, whereas Finrod's "arts" disguising himself and Beren as Orcs were clearly aimed at deception]