Mobile safari vs home-screen webapp

I am developing a webapp for iOS, and I've noticed some weird things between running on mobile safari and running from the homescreen.

Are there any resources that either provide a common interface for going between the modes?

If not, are there any resources detailing all of the differences and gotchas between the two modes?

Things I've run into:

Long-polling is kinda weird. See this example.

window.innerWidth & window.innerHeight are inconsistent.

• Mobile Safari- vertical orientation works as expected, horizontal doesn't
  • Vertical
    • width- 768
    • height- 946
  • Horizontal
    • width- 769??
    • height- 518??
• Web App on Homescreen- These always make sense.
  • Vertical
    • width- 768
    • height- 1004
  • Horizontal
    • width- 1024
    • height- 748

Additional stuff:

I found this and this to be interesting.

This question also sheds some light on weird behaviors.