I want to know the legal and fundamental difference between assignment and sub contract .

Can you give us the context. A subcontract is usually when a contractor contracts with someone else to perform their end of a contract or some part of it. An assignment is when someone transfer a contract to another party. But those are very basic definitions and context matters.

Is this, by any chance, homework?

Assuming it's not, if you contract with someone, you promise them you will do something, in return for their reciprocal promise that they too will do something. This is called "consideration". There must be consideration from each party for there to be a contract.

Let's say the consideration from you is a promise to perform a service, and the consideration from the other party is the promise to pay for it. Assuming that the contract allows you to do so, you may choose to subcontract with someone else to perform the service. Thus there is another contract (requiring mutual consideration between you and the subcontractor). But you are still liable to see that your promise (consideration) for the main contract is performed. If, for some reason, the subcontractor fails to do it, you are still liable.

An assignment, on the other hand, is different. If you assign your duty to perform, as well as your right to the other party's performance (payment, in the example I gave above), the other party to the contract must approve the assignment. If so, the assignee is liable instead of you.