How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.
Application letters and cover letters. Many people believe that application letters and cover letters are essentially the same. For purposes of this handout, though, these kinds of letters are different. The letter of application is a sales letter in which you market your skills, abilities, and knowledge. A cover letter, on the other hand, is primarily a document of transmittal. It identifies an item being sent, the person to whom it is being sent, and the reason for its being sent, and provides a permanent record of the transmittal for both the writer and the reader.