All contract are agreement because contract is an agreement enforceable by law . without agreement contract is not formed.contract is narrow term .It requires legal obligation i.e only commercial Agreement.
all agreement are not contract because agreement is wider term i.e..social, domestic & commercial Agreement. It doesn't require legal obligation.

Introduction:
An agreement is a mutual understanding between two or more parties regarding their rights and obligations. On the other hand, a contract is a legally binding agreement that is enforceable by law. While all contracts are agreements, not all agreements can be considered contracts. In this response, we will delve into the differences between agreements and contracts and explain why not all agreements can be considered contracts.

Agreements:
An agreement is a meeting of minds between two or more parties where they agree upon certain terms and conditions. These terms can be oral or written and may be informal or formal. Agreements are usually based on trust and moral or social obligations, rather than being legally enforceable. They do not necessarily involve consideration (something of value exchanged between parties) and may be binding or non-binding depending on the intention of the parties involved.

Contracts:
A contract, on the other hand, is a specific type of agreement that is legally enforceable. It requires certain elements to be present in order to be considered a valid contract. These elements include:
1. Offer and acceptance: There must be a clear offer made by one party and an acceptance of that offer by the other party.
2. Intention to create legal relations: The parties must intend to enter into a legally binding agreement.
3. Consideration: There must be something of value exchanged between the parties, such as money, goods, or services.
4. Capacity: The parties involved must have the legal capacity to enter into a contract, meaning they must be of sound mind and of legal age.
5. Free consent: The agreement must be entered into freely and voluntarily without any undue influence or coercion.
6. Legality of object: The object or purpose of the contract must be lawful.

Difference:
The main difference between an agreement and a contract lies in their enforceability. While an agreement may be based on trust and moral obligations, a contract is backed by the legal system and can be enforced in a court of law. A breach of contract can result in legal remedies, such as damages or specific performance, whereas a breach of an agreement may not have the same legal consequences.

Conclusion:
In conclusion, all contracts are agreements because they involve a mutual understanding between parties. However, not all agreements can be considered contracts as they may lack the necessary elements for enforceability. Contracts are legally binding agreements that require offer, acceptance, consideration, intention to create legal relations, capacity, free consent, and legality of object. On the other hand, agreements may be based on trust and moral obligations without being legally enforceable.