  We present a demographic analysis of the physical and morphological
properties of $450/850~\mu\rm m$-selected galaxies from the deep observations
of the SCUBA-2 Cosmology Legacy Survey in the Extended Groth Strip that are
detected below the classical submillimeter-galaxy regime ($S_{850 \mu\rm
m}\lesssim 6~\rm mJy$/beam) and compare them with a sample of
optically-selected star-forming galaxies detected in the Cosmic Assembly
Near-infrared Deep Extragalactic Legacy Survey in the same field. We derive the
evolution of the main sequence of star-forming galaxies, finding a steeper
specific star formation rate versus stellar mass at $z>2.5$ than previous
studies. Most faint submillimeter-galaxies fall within $3\sigma$ of the main
sequence, but 40~per cent are classified as starbursts. Faint submillimeter
galaxies have 50~per cent larger sizes at $2<z<3$ than optically-selected
star-forming galaxies of the same mass range. This is also the redshift bin
where we find the largest fraction of starbursts, and hence we could be
witnessing merging processes, as confirmed by the preference for
visual-morphology classifications of these systems as irregular disk galaxies
and mergers. Both populations show an increment towards lower redshifts ($z<2$)
of their concentration in $H$-band morphology, but faint submillimeter galaxies
on average show larger concentration values at later times. These findings
support the claim that faint submillimeter galaxies are mostly a population of
massive dust-obscured disk-like galaxies that develop larger bulge components
at later epochs. While the similarities are great, the median sizes, starburst
numbers and $H$-band concentration of faint submillimeter galaxies differ from
those of optically-selected star-forming galaxies of the same stellar mass.
