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I regularly read articles on The Economist's website. When they refer to themselves, they say "this newspaper". Is this a British usage, or idiosyncratic to what I would call a magazine?

Interesting question. Random thoughts:
Most newspapers are dailies, magazines weekly or monthly. But many local papers in small towns come out weekly. Magazines are on slick paper, papers on pulp. But does that forbid the Economist from calling itself a paper? Add journals, and you find mostly pulp. Mags have a longer deadline, thus more time for research, except on late breaking news, which they can still add depth coverage the following week. Local newspapers ha e longer deadlines, but most avoid muckraking or even intelligent criticism for fear of offending local advertisers. Hmmm...

When they refer to themselves, they say "this newspaper". Is this a British usage, or idiosyncratic to what I would call a magazine?

I would think it's akin to the usage of "this writer" in an editorial. It's a way to emphasize -- or even add gravitas to -- an opinion with third-person construction, to avoid saying "I, I, I," in the process.

Or the regal "we." It's a nuisance that formal theses and dissertations deny the "I" even when promulgating one's personal conclusions. Adds to the turgidity of most of such writing.

While we're on the subject of distinguishing between literary words, can one make a formal, definitive distinction between a diary and a journal?

...can one make a formal, definitive distinction between a diary and a journal?

I can't claim that it's definitive, but here's my take:

Diary - an account of one's thoughts and feelings on events of the day.

Journal - an official account of the events of a society, or of a meeting. Can you imagine calling the publication of the American Medical Association a diary?

Agreed on official journals. I get confused on personal journals. Many "spiritual" advisors of all stripes recommend keeping a journal. Perhaps a diary is a record of the day, and a journal is a deeper introspection or philosophizing?

Perhaps a diary is a record of the day, and a journal is a deeper introspection or philosophizing?

Again, no claims to definity, but I'd put it the other way around. A diary is where you put your deepest thoughts on the day. A journal is a record of the events of the day.

Journal - I saw Jane Doe today.
Diary - I saw Jane Doe today. What is it about her? Do like her, or not?