The difference is who you are writing to. If, for example, you are writing to a friend, you will tend to use an informal level of language. On the other hand, if you wish to write to a bank director, then you will use a formal level of language.
Layout, style and register are the key factors to take into consideration when writing letter in English.
You might want to check out the following site:
ESL EFL English Writing Lesson for Use in Class - Writing Informal Letters - How to Write in English