short letter vs personal letter

short letter and personal letter both are nouns.

Word	Noun	Adjective	Verb	Adverb
short letter	Yes	No	No	No
personal letter	Yes	No	No	No

As nouns, personal letter is a hypernym of short letter; that is, personal letter is a word with a broader meaning than short letter:

short letter (noun)	personal letter (noun)
a short personal letter	a letter dealing with personal affairs