In a unilateral mistake situation, both parties have a mistaken belief. But one party forms its mistaken belief by relying on the other party, and not making any independent examination of the evidence for the belief.
Kastoroff's mistake is unilateral in this sense.
Compare a mutual mistake. In Sherwood v. Walker, the parties were negotiating the purchase of a cow. They parties examined the cow, and each decided, based on their respective examinations, that the cow was infertile.
The cow was in fact pregnant at the time. The mistake in this case is mutual in this sense: each party relied on its own evidence that the cow was infertile; neither party relied on the other's opinion.