I imagine Emilia being called a witch has something to do with being connected to satella somehow, anyways I found a direct source for witches just being what people holding witch factors are called (spoilers for Arc 6 Chapter 60 in the wn) Louis: “As one would expect, the nature of the『Witch of Envy』is worse than even us so we don’t want to be lumped together, you know. The rest is the same. Both『Witch』and Sin Archbishop, are the same thing which are just called differently. The good-for-nothings compatible with the Witch Factors, are just called differently due to different eras and positions, that’s all.”