Using the constructions described in Part I, we compare Stein fillings to Milnor fibers of smoothings for certain rational complex surface singularities. This addresses an important question on the interplay of symplectic and algebraic geometry: every Milnor fiber gives a Stein filling, but the converse is only known to be true in some very special cases. We will explain how to construct "unexpected" Stein fillings via "unexpected" pseudoline arrangements, and show that the topology of these fillings is different from that of any Milnor fiber.