oh sweet thank you for responding so quickly! would it be possible to give an example of a mage and witch way of getting to their goals?

Aside from Arcs and Archetypes and Familiar stuff which can differentiate them apart, Witches tend to be quite practical- They have efficient ideals set in mind about how to do stuff, and will push to do things their way however they can. Mages may be ones to push and insist more in their ideals, if given the chance they will act upon them but pushing the why of their point of view and trying to make others see the way they do to bring change at a greater scale would be more of a primary goal.

For example, in trying to make a friend try out a new meal they like, a Witch may outright prepare the meal for them and expect them to eat it, whereas the Mage will explain how good the plate is and push them to convince them to try it.