At the outset, it should be clear that there are no such remarkable differences between a letter of interest and cover letter. Nevertheless, there are certain aspects specific for both, that make them different from each other.
Both are written to introduce yourself to your prospective employer, and it is attached along with your resume or any other important documents of similar sort.
The basic difference is that, a letter of interest is more like an inquiry, while cover letters expose the qualifications of job seekers in a brief manner. On comparison, you will find out that the similarities have a greater weightage than the differences.
While writing a letter of interest for a job, you first write an introductory paragraph explaining your educational background, and the purpose of writing the letter. The same holds true for writing a cover letter as well.
The introduction is more or less the same in both cases. You will also have to mention your area of interest, and the specific position you are seeking, in the introduction itself.
While writing a cover letter for resume, you need not mention your qualifications in details, because that information will already be provided in your resume. You can just write down the degree you are holding, and the nature of job you are seeking for.
In a letter of interest, you can put forth your inquiries regarding the organization and the possibilities of openings in the present and the future; whereas in a cover letter, we generally do not ask anything from the person we are addressing the letter, rather we disclose our potentials to etch a positive impression on the mind of the reviewer.
In the letter of interest you can ask for conducting a personal interview from the organization but you cannot do so in a cover letter. A cover letter is more precise, and is attached with your resume while applying for a job, or sending a response to an advertisement.
Once you know how to write a letter of interest, you can easily frame the body of the letter by clearly stating your objectives and inquiries.
So, these were the basic differences. Finding out an appropriate salutation for both is utmost important. You can address the person with phrases like, Dear Sir/Madam or Respected Sir/Madam. However, in many fields the affair is more informal, where you can simply greet the person, with a 'Hi' or 'Hello' and then mentioning the name.
However, such salutations are strictly avoided in business dealings, and are used only when the concerned person is known to you.
One important aspect that should not be missed out is mentioning the name, designation, and the official address of the person to whom you are sending the letter. This shows that you are informative about the organization, and it also delivers a sense of respect towards the recipient.
In the closing paragraph, you should mention that the necessary documents and your resume have been attached along. The letter ends with a validation ('thank you', 'sincerely yours'), your name, contact details, and address.
Whether, it's a letter of interest or a cover letter, you must address it in a polite tone, and mention your qualifications very precisely without eulogizing yourself.