Even when looking at the definition, Black Arts and Black Magic by definition are not really different from one another, just magic that are used for negative purpose, The only difference is that Black Arts is the sum of all Black Magic
Even in the raws for what Zeref was described to have mastered the Black Arts, when doing a bit of a rough translation, you get Black Magic most of the time.
Even when Mavis said that Zeref's curse is Anksheram's Black Magic, not Black Arts (not that there is any real difference in what it is called.
Also with the Books of Zere being part of "Black Arts", which this Wikia defines as manipulating life, I do not think that is the case, especially when Eclipse Gate is a magic utilized from the Book of Zeref.
Even the Cult that worships Zeref was described as worshiping Black Magic.
(Note, this is all from official volume translations)
- To merge the pages (Black Magic + Black Arts) and (White Magic + White Arts) together.
- And to restore Zeref's previous edit to what it was