One is "regular" and one is polished and shinier.

Actually, Brilliance is a special finish, "designed to not corrode, tarnish or discolor for a "like-new" look for life, are developed by embedding molecules deep into the faucet's surface, creating a bond that is virtually indestructible. This process is known as Physical Vapor Deposition (PVD)."

That is taken from the Brizo site. Here is a link where you can read the
entire explanation:

Here is a link that might be useful: Brilliance finishes

Brizo is Delta's upscale line.

As stated in the previous thread on these faucets, I have Addison in Brilliant Stainless and Allora in Stainless--I don't visually see any difference.