This is the section of the OED entry on “magic” relevant to the Prince Caspian discussion:
The ‘magic’ which made use of the invocation of evil or doubtful spirits was of course always regarded as sinful; but ‘natural magic,’ i.e. that which did not involve recourse to the agency of personal spirits, was in the Middle Ages usually recognized as a legitimate department of study and practice, so long as it was not employed for maleficent ends. Of examples are . . . the application of a medicament to a weapon in order to heal the wound made by it. These things, if now practiced, would still be called ‘magic’, thought the qualification ‘natural’ would seem quite inappropriate. On the other hand, the ‘natural magic’ of the Middle Ages included much that from the standpoint of modern science is ‘natural’, but not ‘magical’, the processes resorted to being really, according to the now known laws of physical causation, adapted to produce the intended effects.