How do I export a website to an app in safari? There is this feature in iOS 7 called 'save to home screen', I'm looking for something similar on OS X.
The only way I've ever seen this done on OS X is via the Fluid app. Fluid is just a WebKit wrapper around a specific URL and without the browser navigation tidbits in the windowing. It presents the website as an "app" but it's still running in a browser window, albeit one with fewer decorations.
Fluid lets you create a Real Mac App (or "Fluid App") out of any website or web application, effectively turning your favorite web apps into OS X desktop apps.
It's free to use but for $4.99 you can get some features that make it a little cooler. Most importantly you can get per-instance cookie stores so you don't cross-pollute your apps.
I used to use it for Fogbugz and it was alright. Not great, but decent. And I used to get all kinds of questions about the Fogbugz icon in my dock from my colleagues. It's still possible to click away from the main app in the Fluid-ized version of it, leaving you on an unintended web page with not a lot of nav options to get back to the main app. That was probably my biggest gripe with it.