The three types of cover letters are the application cover letter, the letter of interest, and the networking cover letter. Short introductory email cover letters alongside your resume are also considered a form of cover letter.
An application cover letter is used to apply for a specific job, whereas a letter of interest is for expressing interest in working at a company that isn’t currently advertising. A networking cover letter is used to tell one of your contacts that you’re looking for a job and would appreciate their help.