One last question: In order to create a web app does Apple require me to make it available on its app store or can I distribute it independently of Apple? In other words, what Apple says on the link you just provided me with refers to a web app in the app store or to any web app?
The App Store does not distribute Web Apps - only native apps. You MUST distribute it independently of Apple.
Typically, your web site should offer to "save to Home screen". Sometimes they do this with a clever little popup that points to the browser button you need to use to do that.
Mobile Safari can create a Home Screen icon for any website. It just creates a little native wrapper and when you open the "app" by touching the icon, it just launches Safari to your site.
But if the site uses the features shown in the reference above, when they launch it, it can then launch as a "full screen interface" instead of in Mobile Safari. iOS creates a little native wrapper that uses a UIWebView to launch your site into.
If you also use a manifest file, it will cache your pages locally, and you have something that acts more like a native app.