Sites only accessible to people on a network which is linked to the internet are not part of the public internet (for instance, my router's configuration page is most definitely not part of the public internet). A proprietary browser-based application running inside of a corporate network would not be part of the public internet, unless it is specifically designed to be accessible to anyone with a browser. The basic rule of thumb I would use is that something is on the public internet if anyone with a browser in a country with no filtering of the internet can reach it, given the proper passwords and so forth (and without using a VPN or similar tunneling to make it appear that they're elsewhere).
Would you mind explaining the difference between them, other than that one is capitalized while the other is not, then? Focus on how I would be inaccurate if I replaced every instance of "internet" with "Internet" in my previous post.
