A marriage license is known to be a type of document that you need to have when you would like to get married to someone. This means that there are no problems, and you are being allowed by the law to get married to your partner.
A marriage certificate is the type of document that you will have when you need to show proof that you are married to your partner. This can be very crucial, especially for people who would need it. The marriage certificate would need the signatures of the two people who have gotten married.
It would also need some witnesses and some sponsors to make sure that the marriage is valid. There have been cases wherein the marriage certificate is not even valid because of some issues with the people who have witnessed the event and so much more.