  The differences between the inherent stellar populations (SPs) of LAEs and
LBGs are a key factor in understanding early galaxy formation and evolution. We
have run a set of SP burst-like models for a sample of 1,558 sources at
$3.4<z<6.8$ from the Survey for High-$z$ Absorption Red and Dead Sources
(SHARDS) over the GOODS-N field. This work focuses on the differences between
the three different observational subfamilies of our sample: LAE-LBGs,
no-Ly$\alpha$ LBGs and pure LAEs. Single and double SP synthetic spectra were
used to model the SEDs, adopting a Bayesian information criterion to analyse
under which situations a second SP is required. We find that the sources are
well modelled using a single SP in $\sim79\%$ of the cases. The best models
suggest that pure LAEs are typically young low mass galaxies
($t\sim26^{+41}_{-25}$ Myr;
$M_{\mathrm{star}}\sim5.6^{+12.0}_{-5.5}\times10^{8}\ M_{\odot}$), undergoing
one of their first bursts of star formation. On the other hand, no-Ly$\alpha$
LBGs require older SPs ($t\sim71\pm12$ Myr), and they are substantially more
massive ($M_{\mathrm{star}}\sim3.5\pm1.1\times10^{9}\ M_{\odot}$). LAE-LBGs
appear as the subgroup that more frequently needs the addition of a second SP,
representing an old and massive galaxy caught in a strong recent star-forming
episode. The relative number of sources found from each subfamily at each $z$
supports an evolutionary scenario from pure LAEs and single SP LAE-LBGs to more
massive LBGs. Stellar Mass Functions are also derived, finding an increase of
$M^{*}$ with cosmic time and a possible steepening of the low mass slope from
$z\sim6$ to $z\sim5$ with no significant change to $z\sim4$. Additionally, we
have derived the SFR-$M_{\mathrm{star}}$ relation, finding a
$\mathrm{SFR}\propto M_{\mathrm{star}}^{\beta}$ behaviour with negligible
evolution from $z\sim4$ to $z\sim6$.
