Write a Motivation Letter?

To put it simply, a cover letter is more of an introductory letter to your resume to the hiring authority whereas a motivational letter is mainly utilised as how your interests, motivations and aspirations match the academic program you want to study or a job profile you want to apply for. All the elite organizations are in search of individuals who would prove out to be an asset to the company. Thus, it should deliver your intent and excitement using the key feature as your motivation.

For Admission: If you are applying to a university or college to get enrolled in an educational program for any level (undergraduate or postgraduate).
For Training/Internship: If you want to get into a full-time internship with an organization.
For Employment: When you want to apply for a job profile at an organisation.
For Jobs in Social Sector especially NGOs: Non-profit organisations generally demand motivation letter to analyse the interests and intentions of job aspirants.