Star-forming galaxies (SFGs) display a continuous specific star formation rate (sSFR) distribution, which can be approximated by two log-normal functions: one encompassing the galaxy main sequence (MS), and the other a rarer, starbursting population. Starburst (SB) sSFRs can be regarded as the outcome of a physical process (plausibly merging) taking the mathematical form of a log-normal boosting kernel that enhances star formation activity. We explore the utility of splitting the star-forming population into MS and SB galaxies-an approach we term the "2-Star Formation Mode" framework-for understanding their molecular gas properties. Star formation efficiency (SFE) and gas fraction variations among SFGs take a simple redshift-independent form, once these quantities are normalized to the corresponding values for average MS galaxies. SFE enhancements during SB episodes scale supra-linearly with the SFR increase, as expected for mergers. Consequently, galaxies separate more clearly into loci for SBs and normal galaxies in the Schmidt-Kennicutt plane than in (s)SFR versus Mlow * space. SBs with large deviations (> 10 fold) from the MS, e.g., local ULIRGs, are not average SBs, but are much rarer events whose progenitors had larger gas fractions than typical MS galaxies. Statistically, gas fractions in SBs are reduced two-to threefold compared to their direct MS progenitors, as expected for short-lived SFR boosts where internal gas reservoirs are depleted more quickly than gas is re-accreted from the cosmic web. We predict variations of the conversion factor alpha sub(CO) in the SFR-Mlow * plane and we show that the higher sSFR of distant galaxies is directly related to their larger gas fractions.