Query cover letter?

Both a query AND a cover letter? That is genuinely weird. I've never once seen that. Can you quote or link us to the submission guidelines?

The first quote you provide implies to me that by "query" they mean "the work that you're querying" (not an entire manuscript--they'll probably detail how much they want to see, but if they don't I'd send the first fifty pages or so); the second sounds like you're querying UK agencies, as the protocols are different here to the US. Instead of asking for a query letter and nothing else, UK agents usually want a sample of your work (usually around fifty pages), a brief synopsis, and a covering letter (which is not the same as a query letter).

Ah, non-fiction! I should have realised. Sorry.

You query non-fiction in a different way to fiction: you have to write a proposal, which includes an outline, sample chapters, covering letter and so on. You don't write a query for it in the same way you do for fiction. I'm sure it's been discussed elsewhere here.

I think cover letter is basically synonymous with query. At least that is my impression.

"Enclose a cover letter, outline or brief synopsis of the work (with word count if possible), a sample chapter, and a stamped, self-addressed envelope for our response."
-Means to me "include a query, synopsis and sample chapter"

I might be wrong here but if I were to see it from a fiction agent that is what I would assume.

A cover letter isn't the same as a query.

A query letter is designed to sell a book to an agent all on its own. It's the entire package. A cover letter introduces a book proposal package, which would usually include the cover letter, a synopsis, a few sample chapters, and the proposal itself.

In the UK we tend to ask for cover letters plus a writing sample and an outline or synopsis; in the US, for fiction, query letters alone are more usual.