Basic features of spinodal decomposition, on one side, and nucleation, on the other side, and the transition between both mechanisms are analyzed within the framework of a generalized thermodynamic cluster model based on the generalized Gibbs approach. Hereby the clusters, representing the density or composition variations in the system, may change with time both in size and in their intensive state parameters (density and composition, for example). In the first part of the analysis, we consider phase separation processes in dependence on the initial state of the system for the case when changes of the state parameters of the ambient system due to the evolution of the clusters can be neglected as this is the case for cluster formation in an infinite system. As a next step, the effect of changes of the state parameters on cluster evolution is analyzed. Such depletion effects are of importance both for the analysis of phase formation in confined systems and for the understanding of the evolution of ensembles of clusters in large (in the limit infinite) systems. The results of the thermodynamic analysis are employed in both cases to exhibit the effect of thermodynamic constraints on the dynamics of phase separation processes.