Person-to-Person letters

A letter from one person to another is defined as person-to-person letter. These typically deal with personal matters. They can be written formally or informally as the writer chooses.

Letters that are Person-to-Business

A person-to-business letter from a person to a company or organization that relates to business in some way is a person-to-business letter. The writer should keep to a formal style.

Business-to-Business letters

A letter from a business party to another business party is considered a business-to-business letter. These do encompass letters within a company.
"Business" can include any organization intent on a for-profit or not-for-profit product or service.

Letters that are Business-to-Person Letters

A letter from a business to a person, potentially including a customer, is a business-to-person letter. The topic of this type of letter must be about the business between the writer and the reader. "Business" can include any type of organization intent on a product or service, either for-profit or not-for-profit.