Both scholarship and grant are non-repayable financial aids usually disbursed by a public authority,an educational institution or a foundation.
Scholarship is an award for students with a view to helping them financially during their studies. In order to be awarded, students usually have to apply for the scholarship and fulfill several criteria.
There are various kinds of scholarships for different purposes, such as research, study or mobility.
Grant is a project-related financial aid for individuals, small businesses, institutions or other entities. Usually, a grant is given for a specific project during a specific period. In order to receive a grant, one has to apply for it by submitting a proposal to the funder. A funder can be a government, an international organization, an institution, a foundation or a corporation.
As we can see, a scholarship can be regarded as a specific type of grant, whereas grant covers a much wider spectrum of projects.