From the Use Safari web apps on Mac support page:
A web app functions independently of Safari. It shares no browsing history, cookies, website data, or settings with Safari.
Need to use Facebook to stay in touch with that one contact or group? Seems like web apps are the new best way to do this without exposing your activity to Facebook for every page you come across with one of those “Like” button widgets.
On that note, look for websites who generate revenue with your data to start finding ways to diminish the experience when you’re using them from within a web app.