Radical changes in the idea of the organization of intracellular space that occurred in the early 2010s made it possible to consider the formation and functioning of so-called membrane-less organelles (MLOs) based on a single physical principle: the liquid–liquid phase separation (LLPS) of biopolymers. Weak non-specific inter- and intramolecular interactions of disordered polymers, primarily intrinsically disordered proteins, and RNA, play a central role in the initiation and regulation of these processes. On the other hand, in some cases, the “maturation” of MLOs can be accompanied by a “liquid–gel” phase transition, where other types of interactions can play a significant role in the reorganization of their structure. In this work, we conducted a bioinformatics analysis of the propensity of the proteomes of two membrane-less organelles, formed in response to stress in the same compartment, for spontaneous phase separation and examined their intrinsic disorder predispositions. These MLOs, amyloid bodies (A-bodies) formed in the response to acidosis and heat shock and nuclear stress bodies (nSBs), are characterized by a partially overlapping composition, but show different functional activities and morphologies. We show that the proteomes of these biocondensates are differently enriched in proteins, and many have high potential for spontaneous LLPS that correlates with the different morphology and function of these organelles. The results of these analyses allowed us to evaluate the role of weak interactions in the formation and functioning of these important organelles.