The use of a "web browser" has solidified that the content is in fact "the web" in the minds of the general public. But not to worry, because the term "internet" generally still refers to all the technological innovations that bring the content of the web to our displays. IPv6 and future developments to the internet will just need to be called Internet 2.0 instead.
Web 2.0 isn't just social networking style websites, it's about data and content that is always changing and always growing. I tend to look more along the lines of the way the data is handled and modified rather than the content itself, and that has changed. If PHP was used to simply output a dynamic HTML page, the content of that page would remain the same without something to make it change. When PHP is connected to a constantly changing data source like a database, that content can be modified on the fly by whoever is handed the access to it. I believe that level of interactivity seperates the new ways of browsing the web from the old.