How is Arts different from Witch Magic?

I first saw Witch clan magic in 1st ToCS.
But since Arcus unit is available and possibly quite common in more recent series is there any explanation in game about how Witch magic works differently from what Arcus’ Arts does.

My guess is Arcus uses element locked orbment to cast preloaded arts which is like magic from my perspective, in comparison to witch’s magic where maybe they use incantation and convert mana to something specific that they need with/without help from their familiar depending on the kind of magic they are trying to use.

Side question, while Witches are rare, since Arts are like quite common too, is there any reason Witches need to hide their identity / power anymore, like they can just pretend it’s just an Unique Arts or something?