  Star-forming galaxies (SFGs) display a continuous distribution of specific
star formation rates (sSFR) which can be approximated by the superposition of
two log-normal distributions. The 1st of these encompasses the main sequence
(MS) of SFGs, the 2nd one a rarer population of starbursts (SB). We show that
the sSFR-distribution of SBs can be regarded as the result of a physical
process (plausibly merging) taking the mathematical form of a log-normal
boosting kernel and enhancing star formation activity. We explore the utility
of splitting the star-forming population into MS and SB galaxies - an approach
we term "2-Star Formation Mode" (2-SFM) framework - for understanding their
molecular gas properties. Variations of star formation efficiency (SFE) and gas
fractions among SFGs take a simple, redshift-independent form, once these
quantities are normalized to the value of an average MS galaxy. The change in
SFE for galaxies undergoing a starburst event scales supra-linearly with the
SFR-increase, as expected for mergers. This implies a continuous distribution
of galaxies in the Schmidt-Kennicutt plane that separates more clearly into
loci for SBs and normal galaxies than observed in SFR vs. M* space. SBs with
the largest deviations (>10-fold) from the MS, like many local ULIRGs, are not
average SBs, but even rarer events with progenitors having larger gas fractions
than typical MS galaxies. We statistically infer that the gas fractions of
typical SBs decrease by a factor of 2 to 3 with respect to their direct MS
progenitors, as expected to occur in short-term SFR-boosts during which
internal gas reservoirs are drained more quickly than gas is accreted from the
cosmic web. We predict variations of the CO-to-H2 conversion factor in the
SFR-M* plane and provide evidence that the higher sSFR of distant galaxies is a
direct consequence of larger gas fraction in these systems.
