$A,B$ satisfies on the same finite structures implies $A,B$ are logically equivalent?

Question

$A,B$ are two sentences in Predicate Logic, such that for every finite structure $A$ is satisified iff $B$ is satisfied. Prove/ Disprove: $A$, $B$ are logically equivalent.

I assume this contradicts intuition and the statement is false, but I'm lack of a counter-example to disprove this statement.

Answer 1

Say $A$ is "$R$ is a total order with no largest element" and $B$ is "$R$ is a total order with no smallest element"...