grammatical number - What is the difference between a "singular noun" and a "plural noun treated as singular"?

I'd always thought that words like "physics" and "mathematics" were singular: after all, we say "physics is the study of…" etc. But apparently, according to the the comments on this question about "news", each of these words is actually a "plural noun [usually treated as singular]":

(highlighting/ellipsis added by me)
(NOAD = New Oxford American Dictionary)

One, Is this categorization valid? That is, is it correct to say, as the NOAD does, that these words are indeed plural (but treated as singular), rather than to say that they are singular? The accepted answer on that question, by user RegDwigнt, has a different analysis that speaks in terms of “news” being "uncountable", "used with singular verbs", and "etymologically, it used to be a plural form", and thereby carefully avoids addressing this issue, of whether these nouns are indeed plural-treated-as-singular. So my question remains.

Two, If so, what makes these words plural? Is it the fact that they end in s? (Surely "bus" is not plural?) Is it history? (Were they used as plural at some time? How far back in history does one go to decide whether a noun is singular or plural?) Is it the fact that they don't have any distinct forms treated as plural?

Most importantly, why do we even have a grammatical category of "plural nouns treated as singular"? What purpose does it serve, and how are such nouns functionally distinguishable from nouns that are actually singular? When/if the reason is history, is there a rationale for saying "plural nouns treated as singular" rather than "singular nouns that were formerly plural"?

Edit: My question isn't just about "-ics" words, but all words in the category "plural nouns treated as singular" (assuming that the category isn't just -ics words).

Edit 2: The image and part "One" of the question were added later; previously I took for granted that the categorization was valid.