All contracts are agreements but all agreements are not contracts

A contract is a type of agreement or promise or set of promises, which is recognized and enforced by the law. A contract has two distinct parts. First one is that there must be an agreement to do or not to do something. Second one is that the agreement must be enforceable by law. Whereas, an agreement is just an agreement between two parties which may or may not be enforceable by law. It simply means understanding between two parties. A contract is binding but an agreement is not.
Agreements are flexible. When two parties are involved in the contract then they must create a legal relationship between them. Hence, the social agreements such as picnic, invitation, which do not carry a legal obligation, cannot be termed as valid contract.

 A contract to be valid must contain the 8 essential elements. These elements are 1. Offer and acceptance 2. Legal relationship 3. Free consent 4. Competent parties 5. Lawful consideration 6. Two parties 7. Possibility of performance 8. Certainty. If one of the element is missing then it is not considered to be valid. That is it will be just an agreement only. For e.g. If a bank offers you latest schemes  and then you accept it and that scheme contains all the 8 essential elements then there exist a valid contract between you and bank. But if your boss invites you to the party and you accept it then it becomes only an agreement not a contract.

Thus, all contracts are agreements but all agreements are not contracts.