saving password for springboard webapps
It is handled differently because it is two different web engines powering the two.

When you use Safari you're using the newer Nitro-accelerated Javascript engine similar to the WKWebView, you can use in your own apps.

However, when you add the app to the home screen and open it in full screen, it won't be powered by the Nitro-accelerated Javascript engine, and will run in what is essentially the same as the UIWebView, that you can also use in your own apps.

Earlier Apple only allowed third party apps to use UIWebView, and not the newer Nitro-accelerated engine. The reason for the home screen links to be subject to this restriction is probably a leftover from that policy.

However, the reasoning behind why Apple choose to do it this way is impossible to say.