A letter of application is a type of cover letter that accompanies an employment application — typically for civil service agencies, schools, colleges, and other government or quasi-government organizations — and often summarizes information that would have been contained in a resume and may be lacking in the application form itself.
Used in this way, a letter of application is more comprehensive than a typical cover letter and may have skill headings and/or subheadings similar to a resume. Depending upon the application requirements of the organization, a resume may not be accepted in addition to the employment application while a letter of application usually is accepted and may even be required.
A well-designed resume and cover letter combination is usually a better choice to accompany the employment application, if accepted. However, a letter of application can accomplish much of the same goal as the resume by bringing to the forefront your relevant qualifications that may be partially missing or scattered throughout the employment application.
Note: "Letter of application" is sometimes used synonymously with "cover letter."