Complimentary closings are highly standardized and carry little intrinsic meaning. Opinions vary slightly. Here is one summary from
AN ONLINE STYLEGUIDE:
Complimentary Closing
The complimentary closing should
convey the level of formality and degree of personal feeling that
the writer has for the reader.
The complimentary closing (omitted in the simplified letter
format) appears two lines below the last line of text. Its
alignment varies with the format of the letter:
In block letters, the complimentary closing
appears flush with the left margin.
In modified and semiblock letters, the
complimentary appears right of center or may
be flush with the right margin.
Complimentary closings for business letters include:
Sincerely, Sincerely yours, Thank you,
Complimentary closings for informal letters include:
Best wishes, Kindest regards, Regards,
Best regards, Cordially,
Complimentary closings for very formal letters (those
addressed to dignitaries and high officials) include:
Yours sincerely, Respectfully yours, Respectfully,
The word "truly" has
become a cliche and should be avoided in letter closings.