LAEs and LBGs represent the most common groups of star-forming galaxies at high- z , and the differences between their inherent stellar populations ( SPs ) 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 \sim 79 \% of the cases . The best models suggest that pure LAEs are typically young low mass galaxies ( t \sim 26 ^ { +41 } _ { -25 } Myr ; M _ { \mathrm { star } } \sim 5.6 ^ { +12.0 } _ { -5.5 } \times 10 ^ { 8 } M _ { \odot } ) , undergoing one of their first bursts of star formation . On the other hand , no-Ly \alpha LBGs require older SPs ( t \sim 71 \pm 12 Myr ) , and they are substantially more massive ( M _ { \mathrm { star } } \sim 3.5 \pm 1.1 \times 10 ^ { 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 \sim 6 to z \sim 5 with no significant change to z \sim 4 . 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 \sim 4 to z \sim 6 .