Hi, when it comes to the topic of formal letter writing, I could think of businiss letter, recommendation letter, cover letter, and maybe letter to the officials. The question here is if I want to give them a quite general classification, businiss letter should be one big group, how should I classify the others? Is there some commonly accepted way to classify letters? Thank you!
Ahava Yin,

I am not aware of other methods classifying other letters. There are love letters. Letters of condolence. Dear John letters.

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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