In Dou et al. (2021), we introduced the Fundamental Formation Relation (FFR), a tight relation between specific SFR (sSFR), H2 star formation efficiency (SFEH2 ), and the ratio of H2 to stellar mass. Here we show that atomic gas H i does not follow a similar FFR as H2. The relation between SFEHI and sSFR shows significant scatter and strong systematic dependence on all of the key galaxy properties that we have explored. The dramatic difference between H i and H2 indicates that different processes (e.g., quenching by different mechanisms) may have very different effects on the H i in different galaxies and hence produce different SFEHI-sSFR relations, while the SFEH2 -sSFR relation remains unaffected. The facts that SFEH2 -sSFR relation is independent of other key galaxy properties, and that sSFR is directly related to the cosmic time and acts as the cosmic clock, make it natural and very simple to study how different galaxy populations (with different properties and undergoing different processes) evolve on the same SFEH2 -sSFR ∼ t relation. In the gas regulator model (GRM), the evolution of a galaxy on the SFEH2 -sSFR(t) relation is uniquely set by a single mass-loading parameter λnet,H2 . This simplicity allows us to accurately derive the H2 supply and removal rates of the local galaxy populations with different stellar masses, from star-forming galaxies to the galaxies in the process of being quenched. This combination of FFR and GRM, together with the stellar metallicity requirement, provide a new powerful tool to study galaxy formation and evolution.