What's the difference between the two?

Every dead body that is not exterminated becomes one of them. It gets up and kills! The people it kills get up and kill!

Based on my opinion and experience. . .

I believe Adult goes towards a more sexual theme while Mature is more along the lines of blood, gore, violence, and maybe Mature related scenarios?

Hmm, I agree with Nazaki on this matter.

Adult does seem to gravitate more torwads the sexual situations and themes, while Mature is more graphically intense, as it were.

Welcome to Manga-Updates!
If you're new, please read the rules.
If you're returning, please follow them.

Tried to maybe make a cleaner description...