The term 'letter of application' is extremely broad, and can apply in any context in which the writer is making an application. These letters are generally considered to be required to be in a business format, but in practice there's no set form. The cover letter to a job application, for instance, may be written at the discretion of the applicant, and even the information provided isn't required to be in a specific format.
Examples of Letter of Application:
|I've received a letter of application for the position of senior accountant in Arabic.|
The letter of application contained a lot of information about prior experience.
Spelling errors and typos are typical problems in many letters of application.