
What’s the difference between a letter of interest and a cover letter?
I’m not sure if these are the same or if one has more value to hiring managers.

Rather then focus on a letter of interest, I suggest you write what is called a "pain letter." Research a company and find out what their current challenges are (perhaps stock prices have declined) and craft your letter based on what you can do to alleviate that pain.

A letter of interest would express interest of offering your skill to a company, if there are openings in that field. A cover letter is a recap of your knowledge, skills, and experience sent with a bio-summary requesting an interview for an advertised job. Usually sent to HR with request to forward to the Hiring Manager.

A cover letter is given with your resume to introduce yourself.A letter of interest is given after resume. To give more information about yourself

Almost the same thing but you would use the letter of interest of your looking for a job with a company not currently hiring. The cover letter would be included with your application to support other skills, experience, or interest.
Rhonda, I cannot take total credit for this idea. If you are interested Google Liz Ryan and the Human Workplace. She is a no nonsense former HR professional who gives lots of great ideas and suggestions. Good Luck! :)