Nothing. It's just a coincidence that, in English, they sound quite similar.

The "Aryan race" comes from an ancient term used by the Indo-Aryan people to refer to themselves. They settled in a north-east part of India they called Aryavarta. You'll also notice the similarity between "Aryan" and the word "Iran," as the ancient Iranians (who were related) also adopted the word.

Arian Christianity is named after its most famous advocate, a presbyter named Arius. His name has no etymological link to "Aryan".

(Edited: Corrected a mistake)