A displacement reaction is like a stronger person taking the seat of a weaker person on a bench. A neutralization reaction is more like two people swapping seats or joining hands to balance their energy, where no one is kicked off the bench.

In displacement reactions, a high-reactivity metal pushes a low-reactivity metal out of its compound (e.g., $Fe + CuSO_4 \rightarrow FeSO_4 + Cu$). Neutralization reactions follow the form $\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$, which is a double decomposition or double displacement reaction involving the transfer of protons ($H^+$) and hydroxyl ions ($OH^-$), not the displacement of a metal by another metal.

Remember that displacement reactions require one species to be a pure element. If both reactants are compounds (like acid and base), it is typically double displacement or neutralization.