Wheat bran extract is supposedly high in vitamin E, so it’s used as a skin protecting and conditioning ingredient.

What’s the difference between wheat germ and wheat bran?

Both extracts are used in skincare. Wheat is a seed. The germ is the part of the seed that will sprout and grow, whereas the bran is the outer layer of the seed.
The germ has a lot of natural (and essential) oil in it. The bran is very high in non-soluble fibre.