There is an ontology of magic I developed a couple of decades ago, which I never wrote about. The idea is that there are three sets of magical spectrums, representing 7 different types of magical presentation or mechanism.
High versus Low Magic: When you are designing a ritual or spiritual event you have to decide how much you are going to prepare. Is this event rehearsed? Will there be costumes? Will there be elaborate sets or complex props for your event? The more you prepare, the more pageantry, the more visual and auditory elements to your event, the higher the magic.
Dark versus Light magic: The easy way to distinguish these types of magic is by answering the question “Does this magic take power over someone else?” If the answer is “yes” then you are some type of dark magic. If you are doing something to someone without their consent, this is not cool.
Light magic works in cooperation with whoever it is operating on. A prayer to heal someone (who wanted to be healed) would qualify (assuming your religion does not freak out at the idea its sacred acts would be considered magic).
Hard versus Soft Magic: Soft magic is when you make some type of request or cast an intention, that is possible, but perhaps improbable. Here again, many prayers would qualify. Hard magic is when your actions are breaking the laws of physics. Psychic surgery would qualify as hard magic.
Telepathy might qualify as hard magic, teleportation or telekinetics definitely would.
Pop Magic: The last form of magic is not a spectrum at all. Popular magic is tricks or illusionism. This is a different type of event with gravitates towards high and hard magic characteristics.
Perhaps it is less about types of magic as it is descriptions of magic.