Permits are official documents that grant an individual permission to work or perform certain activities. Permits are usually given to render something allowed or legal. For instance, you can be given a driving permit even if you haven't reached a certain age. Permits can also be given to people so they can work for a company for a particular period of time.
On the other hand, licenses are legal documents that give official permission to people to do something, as long as they are ready to comply and fulfill all the requirements that come with it. The common ones are driving licenses, business licenses, product licenses, etc. In most cases, permits are just for a limited period of time, whereas licenses are not temporary, although they can be renewed, and they can be annulled too. While permits are often inspected by the relevant agencies, licenses are seldom inspected. Also, permits usually come with so many restrictions, whereas licenses only have little restrictions.