Agreements are contracts we make with ourselves or others that hold us accountable. In the old days a handshake would be the seal of the agreement and the entire agreement was based on trust. A contract, although exactly the same principle as an agreement, is normally considered a legally binding document.
Another way of looking at the difference between an agreement and a contract would be: A relationship can be considered an agreement, whilst marriage is a contract.
Relationships are based on trust and therefore the agreement is applicable. You are looking for the other person’s word more than any contract they are willing to sign.
More can be found on the agreements within relationships in my book 5 Night Plan where I cover the different agreements and relationship types.