Beginning to define the difference.

<That's difficult to answer, as the quotation doesn't tell me what that "kind of English" is. >

You can read it in the pages of CGEL that you linked us to*. It describes CGEL's use of the term Standard English in said publication.

*Posted below.

MrPedantic wrote:

and 'widely accepted' means? That's the trouble with the quotation: it doesn't tell us in what contexts or by whom that "kind of English" is "widely accepted", or even what that "kind of English" is (except that it's "widely accepted"; which is where we came in). MrP

Here's the context. The description of the the term Standard English that the folks at CGEL are using when they say the above:

Perhaps the most subtle concept we have to rely on is the one that picks out the particular variety of Present-day English we describe, which we call Standard English. Briefly (for we will return to the topic below), we are describing the kind of English that is widely accepted in the countries of the world where English is the language of government, education, broadcasting, news publishing, entertainment, and other public discourse. In a large number of countries (now running into scores), including some where most of the people have other languages as their first language, English is used for most printed books, magazines, newspapers, and public notices; for most radio and television broadcasting; for many or most film scripts, plays, poetry, and other literary art; for speeches, lectures, political addresses, proclamations, official ceremonies, advertisements, and other general announcements. In these countries there is a high degree of consensus about the appropriate variety of English to use. The consensus is confirmed by the decisions of broadcasting authorities about the kind of English that will be used for public information announcements, newscasts, commentaries to broadcasts of national events such as state funerals, and so on. It is confirmed by the writing found in magazines, newspapers, novels, and non-fiction books; by the editing and correcting that is done by the publishers of these; and by the way writers for the most part accept such editing and correcting of their work. This is not to say that controversy cannot arise about points of grammar or usage. There ismuch dispute, and that is precisely the subject matter for prescriptive usage manuals. Nonetheless, the controversy about particular points stands out against a backdrop of remarkably widespread agreement about how sentences should be constructed for such purposes as publication, political communication, or government broadcasting. This widespread agreement defines what we are calling Standard English.

National versus international

Finally, we note that this book is not intended to promote any particular country’s variety of Standard English as a norm; it is to apply internationally...

http://www.cambridge.org/assets/linguistics/cgel/chap1.pdf

<On the other hand, PG is incomplete, because it doesn't deal with anything except its invented "standard English". >

The Cambridge Grammar of the English Language (CGEL) only deals with what the writers of that publication call Standard English. Its writers claim that they give a descriptive treatment of that form of English. Do you agree that it is possible to write about Standard English (see the CGEL definition above) in a descriptive way? Or, do you think that all grammars of Standard English are prescriptive?

MrPedantic wrote:

and 'widely accepted' means? That's the trouble with the quotation: it doesn't tell us in what contexts or by whom that "kind of English" is "widely accepted", or even what that "kind of English" is (except that it's "widely accepted"; which is where we came in). MrP

I add this quote, also from CGEL:

"National versus international

Finally, we note that this book is not intended to promote any particular country’s variety of Standard English as a norm; it is to apply internationally."

http://www.cambridge.org/assets/linguistics/cgel/chap1.pdf

In the article I submit to Descriptive Linguistics Weekly, I include the following sentence:

A few weeks later, I receive the proofs. The editor has changed "Me and Jacques Derrida" to "Jacques Derrida and I".

I call him up.

MrP:  What the *** do you think you're doing with my MS? What's all this "JD and I" nonsense?

Editor:  That's just "Standard English", old boy. We are a prestigious publication. We can't have any of your non-standard stuff in our magazine.

— "Standard English"? Who says it's Standard English? And what gives you the right to decide what's "standard" and what's "non-standard"?

— The CGEL, as a matter of fact, on both counts. Look it up, old chap, if you don't believe me. Chapter 1: see under "Me and Kim". As for "Standard English", that's easy: "The consensus...is confirmed by the writing found in magazines, newspapers, novels, and non-fiction books".

— Well, that's ok. If you leave my text as it is, it will be "the writing found in magazines". So then it'll be "Standard English", by your definition.

— I'm afraid it doesn't work quite like that, MrP. Read on: "[and] by the editing and correcting that is done by the publishers of these." So you see, I outrank you, old boy. I have edited and corrected your text; ergo, it's now Standard English.

— Wait a minute. I ask you why you've corrected my text. You say, because it wasn't standard English. I then ask you, what makes your version standard English. And you say, because it's the version I've corrected your text to. Is that what you're saying?

— In a nutshell, old boy, yes.

— <expletives removed by mod> <hangs up>

— [To self: ] Now there's a curious thing. It says in the CGEL that "writers for the most part accept such editing and correcting of their work"...but MrP didn't sound very happy at all...

MrP