The underlying logic of most traditional witchcraft is animism. Animism in the sense that the physical components of witchcraft have spiritual agency and intention that the witch is able to cajole one way or another to their purpose. And furthermore, the power and agency of any target is taken to account as potentially having innate or obtained protections that could backfire should the spell be wrong somehow. Whereas much of modern witchcraft is not animist, and the only figure with agency are the humans involved: the witch and their target–a target whose will is assumed so weak that it must be protected by maxims.
These stark differences dog much of the interwitch discourse. The opposite world views are chocked up as elitism by the modern witches against the traditional. And traditional witches dodge the insult that they are still in training wheels for using tools and components. The modern witches say my greatest witch tool is my mind whereas a traditional witch may say a tool is a useful constructed object (usually manmade but a few animals make tools too). Or the idea that magic does not work without taking major mundane actions to further them. That requirement coming from there being less effort taken in the spell itself and perhaps no assistance petitioned from the spirits of the materials employed so much the effort is taken non mystically. Most modern witches say spell components are mere props. Whereas traditional witches often befriend their spell components.
I will never say modern witchcraft doesn’t work. It follows its own logic premised on inspiration. Verily inspiration is quite powerful and I won’t knock it. And the logic of inspiration carried out is acting in accord which is very effective combined with the tools of theatrics based off of personal correspondences. It may even be possible to reconcile the two.
Many traditional witches in addition to their animistic approach also follow through with acting in accord which doesn’t have to hurt, but can limit the possibilities noticed for the result or can alternately pave the way to allow the animistic powers to flow more productively.
Additionally, traditional witches can find ways to work without tools and materials after learning to contact the spirits of those materials indirectly without the presences of the objects for immediate relating. Witches can use the animist power of words or strengthen their ability to harness fate to be able to do it with energy or psychic ability. But certainly it’s not only their own intent carried out, but a cooperation or dictation of the other powers that be to that end.
So basically, there is more than one system. I use the terms modern and traditional merely as stand in identifiers. Of course there are those that identify with one or the other but have differing metaphysical practices than I used for demonstration purposes.