Not exactly, a contract must bind both parties to do something. You cant have a contract which states "you give me money and you dont say anything about it." It must also bond the other side: "and in return I will not sue you for piracy committed on the date of..."
You missed chacham's point. You are right that both parties have to agree to make a contract. But on top of that it's not a contract unless both sides get something out of the deal. If you sign a piece of paper to exchange $10 for nothing, it's not a contract.
