We address in detail the problem of true morphological phase separation (MPS) in three-dimensional or (2+1)-dimensional unstable thin liquid films (>100nm) under the influence of gravity. The free-energy functionals of these films are asymmetric and show two points of common tangency, which facilitates the formation of two equilibrium phases. Three distinct patterns formed by relative preponderance of these phases are clearly identified in "true MPS". Asymmetricity induces two different pathways of pattern formation, viz., defect and direct pathway for true MPS. The pattern formation and phase-ordering dynamics have been studied using statistical measures such as structure factor, correlation function, and growth laws. In the late stage of coarsening, the system reaches into a scaling regime for both pathways, and the characteristic domain size follows the Lifshitz-Slyozov growth law [L(t)∼t^{1/3}]. However, for the defect pathway, there is a crossover of domain growth behavior from L(t)∼t^{1/4}→t^{1/3} in the dynamical scaling regime. We also underline the analogies and differences behind the mechanisms of MPS and true MPS in thin liquid films and generic spinodal phase separation in binary mixtures.