"Every promise and every set of promises forming the consideration for each other is an agreement" - Sec 2(e). It means whenever one or more persons promise to each other to do or not to do something that is an agreement.

On the other hand according to the contract act 1872 a contract is, "An agreement enforceable by law." - Sec 2(h). According to Salmond, "A contract is an agreement creating the defining obligations between the parties". According to Sir William Arson, "A contract is an agreement enforceable at law made between two and more persons by whom rights are acquired by one or more by to act or forbearance on the part of the others.
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Agreement is emerged from willingness of both parties to do or not to do something. As no legal obligation is required here so just any two parties can mutually dispute on any matter. Agreement is emerged this way.

 But all true contracts begin with an agreement.
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An agreement may be legal or illegal. As it is not bound by the law it needs not to follow the rules.

 On the other hand only legally enforceable agreement is contract. So it can never be illegal.

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Agreement may be against of human rights. It will create no problem because the parties will not seek help from the law.

 A contract can never be against of human rights.

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Purpose of an agreement can be illegal.

 But purpose of a contract can never be illegal.

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An agreement can be with an impossible matter. As it is not banded by the law people can make agreement on any matter.

 Contract cannot be with any impossible matter.

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Agreement between two parties does not create any legal obligation or relationship.

 As contract is enforceable by law its obvious purpose is to create a lawful relationship.

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An agreement may be expressed or implied.

 But a contract must be expressed and clear that no ambiguity can occur.

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An agreement is not dependent on contract.

 But a contract is dependent on any agreement.

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There is no obligation to write or register an agreement.

 Each and every contract must be written and registered.

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Any two parties can make an agreement.

 But the parties of contract must be capable of contracting.

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All agreements are not contract.

 All contracts are agreement.