The paper presents a review of results concerning the non-conventional dynamical condensation versus conventional Bose-Einstein condensation, including the case of generalised van den Berg-Lewis-Pulé condensate. The review is based on detailed discussion of two models: a simple toy model and the Bogoliubov Weakly Imperfect Bose-Gas model, which was invented for explanation of superfluity of liquid 4 He, but which is also instructive for analysis of non-conventional condensation regarding some recent interpretations of experimental data.