Overall, the manga of Black Butler often provides more detailed character development and storylines. The anime, on the other hand, might make certain adjustments for better visual presentation and pacing.
The Black Butler anime's ending doesn't have an exact equivalent in the manga. It deviated from the manga's plot and provided its own conclusion for the animated adaptation.
In general, the Black Butler anime adheres pretty well to the manga. Some scenes might be re-arranged or expanded for better animation and pacing, but the core story remains intact.
In many ways, the Black Butler anime differs from the manga. The character development might be a bit different, and some plot points could be emphasized or downplayed. Also, the art style and animation can give a distinct feel.