I'm not really very familiar with SolidWorks Simulation, so I may get some of this wrong.
Static is limited to linear material properties. It does actually give you a few non-linear capabilities, like contact and large deflection analysis.
Nonlinear static lets you use nonlinear material properties. It also allows you to apply loads in a time-like way (pseudo-time). So you could clamp a part to another with a given force, then apply another force to see if the part will move. You can ramp your forces up and down as required. None of this happens in "real" time. It ignores inertia.
Nonlinear dynamics is working in "real" time. If you apply a step load to cantilever for instance, and follow it long enough, the cantilever would vibrate just as in real life.
Yuvaraj, might be worth describing your problem and we can answer in context of your problem and what assumptions would be eliminated by study.
Jerry's definitions are good though.
linear = small displacement, linear material, no inertia
nonlinear static = large displacement, nonlinear material, no inertia
nonlinear dynamic = large displacement and rigid body motion, nonlinear material, inertia and time are part of the load definition
i would also sneak linear dynamic between nonlinear and nonlinear dynamic for situations where the time effect is of importance but you can work with linear materials and there are no impacts. that being said, impacts can be input through pulse type loads.
the help has some good info