A grant is a sum of money you receive for any purpose. It's often given to students so that they can pay for food, accommodation and so on while they're studying, but not always. For example, if your house is in need of urgent repair, the government might give you a grant to help you repair it.
A scholarship is more specific : it usually allows a specific student to study at a specific institution. Sometimes, you don't even see the money - the student simply takes the course without having to pay tuition fees or takes a course at a reduced fee.