thermodynamics - Increase in entropy principle

If we consider a system to undergo an irreversible process from state 1 to state 2 and a reversible process from state 2 to state 1, then through Clausius inequality

$\int_{1}^{2} \frac{\delta Q_{irrev}}{T} + \int_{2}^{1} \frac{\delta Q_{rev}}{T} \leq 0$

$\int_{1}^{2} \frac{\delta Q_{irrev}}{T} + S_1 - S_2 \leq 0$

$S_2 - S_1 \geq \int_{1}^{2} \frac{\delta Q_{irrev}}{T}$

$\Delta S \geq \int_{1}^{2} \frac{\delta Q_{irrev}}{T}$

Does this mean that the entropy change for a reversible process is greater than that of an irreversible process? I'm convinced I am wrong because my notes say otherwise but isn't Δs the entropy change of a reversible process and ($\int_{1}^{2} \frac{\delta Q_{irrev}}{T}$) the entropy change of an irreversible process?