Well, the web app and web site is a very broad topic and no conclusion can be made in a positive manner out of the long term discussion. But, as always, I would suggest that you give
MSDN a thorough look to learn the difference between Web app and Web site[
^].
After that, the deployment is pretty easy, you paste the binaries (assemblies) into the bin folder. Then, the rest of the pages depend on your framework. ASP.NET exposes two different frameworks (Web Pages and MVC)*, both are based on different conventions. Mostly the Web Pages framework is targeted as Websites, and MVC is targeted for Web application. Before, I tell how to deploy the source code, if you want to learn the MVC itself, please read:
Novice to MVC? Read this…[
^]. Also, for novice ASP.NET MVC developers I have another article, that targets the beginners, you might be interested in it:
Understanding ASP.NET MVC using real world example, for beginners and intermediate[
^].
That said, you need to know that the application consists of assemblies, HTML files, code-behind (the C# files). Now, the deployment (if done manually; I don't know of any automatic process) of the website to web app would be like,
bin --> bin
HTML files (.cshtml or .vbhtml) --> Views/ControllerName/(as HTML files)
Code behind (.cs) --> Controllers/(in the form of Controllers for your app)
Finally make a few changes to your web.config as per SmartStore requires you to, and you're done. :)
*
Only until ASP.NET 4.5, ASP.NET 5 introduces ASP.NET MVC 6 which holds the power of ASP.NET Web Pages, ASP.NET MVC and ASP.NET Web API with SignalR and Entity Framework as a plus feature. Also the Web Forms is not included.