The world wide web is a group of standards (HTTP, HTML/W3C's area)
When you think of the internet as Google, Facebook or your obscure pickle worshiping online shrine website, yes that is the internet and the world wide web. The World Wide Web is a subset of the internet. The internet is a much broader group of things. Simply all the internet is a network routing messages and packet pushing all over connected computers. The world wide web is something way to hard to describe in such few words. This is a fact, not a opinion :D
The distinction between the World Wide Web and the Internet is still very relevant. The Internet is the system of interlinked computer networks that provides the hardware and bandwidth that the World Wide Web runs on. The World Wide Web is a service (application) that runs on the Internet. It's the collection of documents, multimedia resources and other assets that are accessed via hyperlinks over the Internet. The distinction between the World Wide Web and the Internet is very valid.
I think the World Wide Web and the Internet are essentially one and the same, the terms can easily be used interchangeably, there is only one Internet to access and no matter what you call it it's the same exact thing so I don't see there as being any difference between the two names at all.
The Internet has seemingly become synonymous with the world wide web, and I would personally be unable to describe the difference between the two. I believe that for all intents and purposes they are the same, and any sort of nitpicking about the differences is worthless banter about semantics and triviality.
I really don't see a different between the world wide web and the Internet. I assume each stands for something slightly different, but that makes no difference to me, the average user. I feel like people who know the difference between these two terms are more affluent in computer services.
I do not think that there should be distinction between the World Wide Web and the Internet. While technically each term describes a factor of what makes up the online world, they are both related to each other and do not exist without one another. So I don't think there should be an extinction.