Yep - magic can mean a lot of things depending on context. You usually hear about spells and such when it’s an exercise in intent projection - trying to send some signal into the universe or whatever to align with your personal goals. The other definition you mention is more about unexplained phenomena. There’s definitely others, too.
I probably should have asked this first - when you say getting more into witchy stuff, what does that look like? Say you decide to start tomorrow - what does tomorrow look like for you?