Topology Optimization methods (Density and Level Set) relate to the Immersed Boundary Method (I.B.M.) in that the shape is approximated using an auxiliary field (density-field or level-set function). Using this method, the application fixes the mesh during the optimization process and optimizes the shape by distributing the material layout within a given design domain. Topology Optimization is very convenient when you expect significant changes (hole nucleation, merge of members, etc).

Shape Optimization methods relate to a body-fitted method in that the shape is explicitly defined by the mesh. Using this method, the application optimizes the design by moving the mesh nodes. Shape Optimization is a sort of morphing without the need to define any parameter. By contrast to Topology Optimization, the calculation of certain quantities, such as stress, is more accurate. Shape Optimization is convenient when you expect moderate modifications while keeping the same topology (no hole, no merge).