A single website or seperate websites?

I've created a asp .net web app which uses a business logic layer. The web app users css for styling. I want to create another website that uses the exact same business logic layer but looks completely different. Basically if a user was to visit each site, they'd be unaware that they actually share the same business logic. What would be the best approach for this? Having a single web app but using different css? Or creating a another web app for the second site? The sites would share code but I want to use different controls in another.