What is the difference between the Pdelta and a Nonlinear Analysis ? I tried both on my structure and did not observe any significant difference.

In a Pdelta analysis you are accounting for the second order effects resulting from displacements ( normally Large delta and Small delta ). However if the structure or loading is such that the analysis results in large displacements, then in addition to accounting for the effect of these secondary forces, one should also account for the fact that the stiffness of the structure may change significantly as it deflects. Nonlinear analysis allows you to account for such changes in stiffness with application of load. Depending on the nature of the problem, the loads should be applied in steps while the stiffness is adjusted multiple times within a load step to arrive at a converged solution.

In your structure, nonlinear effects may not be that significant and hence you may not have noted a significant difference between a second order and a nonlinear analysis. If the strucrure stiffness would have changed significantly, you would have seen the effect in results.