The difference between agreement and contract are given below:

What is it? :
Agreement - A mutual understanding or meeting of the minds between two or more parties.
Contract - A legally binding document that outlines the terms and conditions of an agreement.

Is it legally binding? :
Agreement - No.
contract - Yes

Type :
Agreement - Mostly informal
Contract - Formal

Usage:
Agreement - There are primarily used by friends, family, etc.
Contract - They are mainly used for business activities.

Scope :
Agreement - Has a broader scope.
Contract - Has a narrower scope.

Consideration :
Agreement - Agreements can be formed without consideration.
Cotract - There should be some consideration while forming a contract.

Defined under:
Agreement - Section 2 (e) of the Indian Contract Act, 1872.
Contract - Section 2 (h) of the Indian Contract Act, 1872.