Meaning of various valedictions or closing expressions

Related to, but I believe distinct from, the following questions:

• What does the "yours" in "yours sincerely" mean?
• Which expressions can be used to close an email?

What do various valedictions mean in the context of a written (business) letter, and what do the following typically convey?

1. Best,

   Best what? Is this short for best wishes or best regards? If this is a shortening of the phrase, is it rude?

2. Regards,

   Also unclear what this means in a valediction. Does this mean I'm thinking of you?

3. Best Regards,

4. Cordially,

5. Good Wishes,

6. Many Thanks,

   Is this more or less formal than "thanks"?

7. Thanks,

   Am I right that this is a rude way to close a letter?

8. Most Sincerely,

   Is this expression too much?

9. Sincerely,

10. Thank You,

11. Yours truly,

I end almost all my emails with one word only: "Bill". When I applied for a teaching job last year, I ended it with "Sincerely yours," & when I send letters to some clients, I end them with "Bill Franke, Medical Editor". "Thanks; Many Thanks; Best; & Regards" are all informal but not rude. They're not my style, so I never use them. All the rest but #8 are formal & polite, & they're appropriate for business letters: but different countries have different styles. "Most sincerely" is obsequious & should always be avoided: you're either sincere or not sincere, never some degree of sincere.

All valedictions mean the same thing: "Bye-bye. Letter's over. Hope you like what I said and that you hire me or buy my product or give me whatever else I asked for." They're just socially approved formulas for various types of letters. Check a How to Write a Business Letter manual for the countries you want to send letters to. You'll see that styles differ for the UK, the USA, and Hong Kong. Use the one that's appropriate for the letter you're writing.

There are others that are popular, e.g., "Yours faithfully" (a UK valediction, I believe)

Nos. 1 and 7 are informal, but certainly not rude. I wouldn't use those shortened forms with people I didn't know very well, but they work nicely with close acquaintances, when more formal options like #3 and #11 begin to sound awkward.

No. 8 is rather formal and perhaps old-fashioned, and could be too much, but I don't think anyone would be put off by it.

No. 5 should probably be expressed as "Best wishes," not "Good wishes,".

Generally speaking, valedictions like these can be split into two categories: such as formal and informal, polite and friendly, or standard and unique. Often, people will use the former categories (formal, polite, standard) when writing to someone they don't know very well, or someone in a position of authority, and the latter categories (informal, friendly, unique) when writing close friends or peers.

I'd classify Nos. 3, 4, 9, and 11 as formal, polite, and standard, while Nos. 1 and 7 would be informal and friendly, along with other sign-offs such as "Cheers,".

Nos. 2 and 10 could bleed into either category.

Toodles,

J.R.