Why all contracts are agreements but all agreements are not contracts?

“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 the Indian Contract Act, “A contract is an agreement enforceable by law”. Obviously, an agreement is a prerequisite (i.e.., essential elements) for the formation of the 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 the 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