Two states A and B are distinguishable if there exists some string w belongs to $\sum ^{*}$
such that $\delta ^{*}(A,w) \in F$ and $\delta ^{*}(B,w) \notin F$.
Then we say A and B are distinguishable by string w.
Now here what is the definition that two strings are distinguishable ?
if we just start with initial state and go with the pair of strings we find both the pairs are either going to final state or both going to non final state.
