The classification of a letter as formal and informal is on the basis of its tone and style. A cordial friendly tone, an easy style of language make the letter informal. Business letters adopt a less formal tone than governmental/ bureaucratic I correspondence.
The classification of letters as official, demi-official or personal depends on the relationship between the people who exchange letters. Usually, this is related to hierarchical positions and social strartification.
Based on content a letter can be a good-news letter or a bad-news letter.