This is mostly an academic question.
Suppose you have a book. Maybe something like the emacs manual. The book is divided into sections and subsections. Those sections have "next" and "previous" relationships with their adjacent sections, and I suppose that's what the W3 was talking about when they wrote about link types:
Next. Refers to the next document in a linear sequence of documents. User agents may choose to preload the "next" document, to reduce the perceived load time.
So far so good.
But nobody uses it that way. On the contrary, it seems that Google has redefined "next" and "prev" so that they mean essentially, "treat all these as one page."
Now, if you choose to include rel=”next” and rel=”prev” markup on the component pages within a series, you’re giving Google a strong hint that you’d like us to Consolidate indexing properties, such as links, from the component pages/URLs to the series as a whole
That's wonderful news for the good people whom expediency has driven to serve in pieces what is properly a single unit.
But the W3 definition is so buried under this excitement about consolidated rankings, that as recently as September 16 of an unspecified year, some practitioners of SEO embraced it as a "new HTML element":
Now we can use a new HTML element known as rel=”next and rel=”prev”.
So my takeaway is that one should not use rel="next" and "prev" as the W3 describes, if your pages are pages for a reason.
Is this correct?