congratulations letter vs congratulatory letter

congratulations letter and congratulatory letter both are nouns.

Word	Noun	Adjective	Verb	Adverb
congratulations letter	Yes	No	No	No
congratulatory letter	Yes	No	No	No

As nouns, congratulations letter and congratulatory letter are synonyms defined as:

congratulations letter and congratulatory letter: an official letter in which one's achievements are recognized and honored.

congratulations letter (noun)	congratulatory letter (noun)
an official letter in which one's achievements are recognized and honored.	an official letter in which one's achievements are recognized and honored.