What type of mistake occurs when one party is mistaken while the other is not?

The scenario described pertains to a unilateral mistake. This type of mistake occurs when one party to a contract has a misunderstanding about a fundamental aspect of the agreement while the other party is aware of the true situation. In legal terms, this often means that one party is under a false impression concerning an essential fact, leading that party to enter into the contract without full knowledge or consent.

For example, if a seller believes they are selling a rare book while the buyer knows it is a common text, the seller's misunderstanding constitutes a unilateral mistake. The contractual obligation may not be enforceable if the mistaken party, typically the one who is misled, had no opportunity to clarify the existing condition or fact before entering into the agreement.

Other terms presented do not align with this specific situation. A common mistake involves both parties sharing the same incorrect belief about a fact that is essential to the agreement, while a mutual mistake means that both parties hold differing beliefs regarding an essential fact, but they are both mistaken. An agreed mistake might suggest a mutual understanding that is flawed, but that terminology is not formally recognized in contract law the same way as the others. Thus, the definition of a unilateral mistake most accurately captures the scenario described in the question.