“All contracts are agreements but all agreements are not contracts”- the statement has two parts.
(a) All contracts are agreement: As per section 2(h) of Indian contract Act, “A contract is an agreement enforceable by law”. Obviously an agreement is a pre requisite (i.e.., essential elements) for formation of contract. An agreement clubbed with enforceability by law and several other features (i.e.., free consent, consideration, etc..,) will create a valid contract. Therefore, obviously all contracts will be agreements.
(b) All agreements are not contracts: As per section 2(e) of Indian contract act, “An agreement is a promise and every set of promises, forming consideration for each other”. Thus, a lawful offer and a lawful acceptance create an agreement only. Therefore all agreements are not contracts.
Conclusion:
Contract = Agreement + Enforceability by law.
Agreement = Offer + Acceptance.
Thus, all agreements are contracts but all agreements are not necessarily contracts.