First, you should work through the tutorials and read the sections in the manuals/help on non-linear static and advanced non-linear static analyses and how to set them up.
Let's tackle the second picture (Load Set Options for Nonlinear Analysis) first, since it is the most simple and straight forward. This form is for a non-linear static analysis. The NUMBER OF INCREMENTS field is simply the number of load step divisions you want. The solver will simply divide the applied loads by this value, then apply the loads, solve for displacements, and apply the next bit until the entire load has been applied. I generally use this for large displacement problems. It works well with gap elements but does not recognize non-linear contact regions. The MAX ITERATIONS PER STEP designates how many iterations the solver will attempt before it decides that the solution will not converge for that load step.
The first picture (NXSTRAT) is for either advanced non-linear static (SOL601) or non-linear dynamic (SOL701) solutions. This form allows you to set up the total number of steps and the time increment for each step. You use this, in conjuction with loading functions to apply time-dependent loads, displacements, etc. onto your model. The OUTPUT EVERY NTH STEP tells the solver how often to produce output data. This allows you to get results for the various parts of the loading, unloading, and response spectra.
I hope this helps,
"On the human scale, the laws of Newtonian Physics are non-negotiable"