A concordat is an agreement between parties, especially between nations or between a church and a nation. A concordat is official, written, and signed.
When there is concord, there is agreement. That can help you remember that a concordat is a type of agreement between two or more parties. The earliest concordats were between the Roman Catholic Church and various governments, but a concordat can exist between any two entities, including two nations. When there's a concordat, the parties sign a contract and agree to do something. A treaty is a type of concordat.