We explore the properties of high-redshift Lyman-alpha emitters ( LAE ) , and their link with the Lyman-Break galaxy population ( LBG ) , using a semi-analytic model of galaxy formation that takes into account resonant scattering of Ly \alpha~ { } photons in gas outflows . We can reasonably reproduce the abundances of LAEs and LBGs from z \approx 3 to 7 , as well as most UV LFs of LAEs . The stronger dust attenuation for ( resonant ) Ly \alpha~ { } photons compared to UV continuum photons in bright LBGs provides a natural interpretation to the increase of the LAE fraction in LBG samples , X _ { LAE } , towards fainter magnitudes . The redshift evolution of X _ { LAE } seems however very sensitive to UV magnitudes limits and EW cuts . In spite of the apparent good match between the statistical properties predicted by the model and the observations , we find that the tail of the Ly \alpha~ { } equivalent width distribution ( EW \gtrsim 100 Å ) can not be explained by our model , and we need to invoke additional mechanisms . We find that LAEs and LBGs span a very similar dynamical range , but bright LAEs are \sim 4 times rarer than LBGs in massive halos . Moreover , massive halos mainly contain weak LAEs in our model , which might introduce a bias towards low-mass halos in surveys which select sources with high EW cuts . Overall , our results are consistent with the idea that LAEs and LBGs make a very similar galaxy population . Their apparent differences seem mainly due to EW selections , UV detection limits , and a decreasing Ly \alpha~ { } to UV escape fraction ratio in high SFR galaxies .