S is defined as the number of microscopic states that are compatible with a given macroscopic condition. So, S is proportional to the variety of microscopic states compatible with a given macroscopic situation. This is maximized at equilibrium. Taking stock here, we can note that entropie is informational in that it involves configurations that affect the efficiency of the conversion of energy gradient to work. Gradients are orderly, and must be in order to be harnessed to work.
S too is informational, involving the configurations of microscopic particles.
In each case, entropie or S, the entropy is a matter of missing information. In the second case this missing information is that which might have prevented the unconstrained diffusion of energetic particles. In Boltzmann the missing information relates indirectly to missing barriers to diffusion and directly to the uncertainty of configuration of the microscopic particles. With entropie the missing information relates to missing barriers to undirected dispersion of gradient, and also to information affecting the rate of gradient utilization. In both cases, if all information is missing the entropy will be maximized as the energetic particles just diffuse away.