Step 1: Understanding the reactions.
The dye test is a method to distinguish between different amines based on their reactivity. \( p \)-toluidine and benzyl amine exhibit different behaviors during the test, which allows their differentiation.
Step 2: Conclusion.
Hence, the dye test is the correct way to distinguish between \( p \)-toluidine and benzyl amine.
Final Answer:
\[
\boxed{B}
\]