Formal letters are sent to organizations, government departments, chair holders, etc to make complaints, requests, inquiries, orders etc. In case of formal letters, the person to whom you are addressing the letter is not a friend or any other person known to you. Your tone is full of respect making use of formal words and sentences to create a nice impression on the recipient.
Informal letters are written to friends and relatives. The purpose of writing a letter is not to make a complaint or inquiry, and the tone is also casual. The words used can be colloquial and slang, and you are not there to create an impression. Informal letters can be considered a freestyle swimming where you are free to write in the style and tone as you wish. There is no set format, and there is no need to be using formal style and tone.