Strictly speaking, a letter of interest is used when you are inquiring about a position or positions which have not been specifically advertised by the school. You will, however, find letter of interest and cover letter used interchangeably.
A cover letter is the letter which you send along with your application, resume and whatever supporting materials the school has specified.
Why do the two letters seem to be the same thing and have the same use? Simply because employers don't always know which one to ask for. Consequently they will ask for a letter of interest when they really mean a cover letter. Here's how to write each kind of letter.
The Letter of Interest Strictly speaking, as we noted above, a letter of interest is what is called in the trade a 'prospecting letter'. No specific job has been advertised at the school to which we plan to send a letter of interest. It just happens to be an institution in which you are very interested. You also feel that your credentials and experience might be a good match for the school's requirements. So you are writing a letter of interest which is unsolicited.
Follow this guide to produce a letter of interest. Don't simply copy and paste letters which you see on the web. Always edit and customize your finished letter so that it fits the school to which you are planning to send it.
Lastly, make sure that your letter is perfect. No typos. No mispellings. Perfect. After all, this is the first impression a prospective employer will have of you. Make it a good impression. If your materials are not flawless, be assured that your competitors' materials will be.
Where the distinction between letters of interest and cover letters blurs is when a school asks you to send a letter of interest. What they probably mean is a cover letter.
The Cover Letter You write a cover letter to accompany your formal application for a position. The school has specifically instructed you to send them letters of reference, a resume and copies of your academic transcripts. This is the first thing whoever opens the envelope will see. A cover letter must be perfect. It must be well-written and fit one page.
As with the letter of intent, perfection is a must. Use these sample cover letters as models. Again, do not copy and paste. Customize your cover letter to fit your specific requirements.