In Agents of S.H.I.E.L.D., and again in WandaVision and Doctor Strange in the Multiverse of Madness, the book called "the Darkhold" is used and heavily affects the plot.
However, they both have different appearances, as seen below:
What is actually different about these two books? It seems as if they contain the same powers, so why are their appearances different?
The book, the Darkhold, as explained in Doctor Strange in the Multiverse of Madness is actually a copy of the spells carved into the walls at Mount Wundagore. As such the physical difference between the two books is easily explained by them just being two separate copies of the same spells. They're not the same physical book but the contents are the same.
Wong: The Darkhold was a copy!
Wanda: A copy?
Wong: Legend speaks of a mountain with the wretched spells you seek carved into its walls. It's there the Darkhold was transcribed. Mount Wundagore.
Doctor Strange in the Multiverse of Madness
The book Marvel Studios’ The Marvel Cinematic Universe: An Official Timeline documents the events, characters, and items that belong to the main MCU timeline, also known as “616” or the “Sacred Timeline.”
This book does not feature anything from Agents of S.H.I.E.L.D. or Runaways, which implies that they are set in alternate timelines from 616. Therefore, the Darkhold that appears in those shows is not the same as the one that appears in WandaVision and Doctor Strange in the Multiverse of Madness, and that explains why they have different appearances.
