Magic Theory is the "Theory" of how magic works. It is academic in nature, dealing with the structure of magic and its core rules. It does not include any flavor or history. You would use this when trying to design a new spell or ritual. If used to identify a spell, it would be a scientific identification. "That would be an elemental creation spell, focused on force and fire."
Adding the word magic into theory nets you...
QUOTE
Magic theory is the study of the theoretical foundations of magic, and of practical techniques for their implementation and application. It is frequently described as the systematic study of processes that describe, transform, and direct magic.
Magic Background on the other hand is the key events, information, and effects that relate to magic. As an example, computer background would cover key events in the past that relate to computers today along with things like all the keyboard shortcuts and a few little 'tweaks' to make things run a little faster. It is focused on useable knowledge of the near past and today, unlike theory which is focused on future possibilities and core principles. It is a 'jack of all' skill, as long as things relate to how magic works and key events in its past. Pretty much the magical trivia pursuit skill. If used to identify a spell, it would give a trivia identification, but would not work on unique spells that well. "The mage cast 'ball of abyssal flame'"
Magic History would be the other skill in the trilogy, which I don't have to go into since everyone knows what history is.
------------------------
To help, we will use Engine Theory, Engine Background, and Engine History in a quick example.
-You would use Engine Theory as an assisting knowledge if you were: Designing a new engine
-You would use Engine Background as an assisting knowledge if you were: Modifying an existing engine for location or performance
-You would use Engine History as an assisting knowledge if you were: Trying to fix an engine and only had access to old (junkyard) parts "The LE7 uses the same crank as the old LJ4, so we can use that one"