We present a study of the intersection between the populations of star forming galaxies selected as either Lyman break galaxies (LBGs) or Lyman-alpha emitters (LAEs) in the redshift range 2.9 − 6.7 and within the same volume of universe sampled by the Multi-Unit Spectroscopic Explorer (MUSE) behind the Hubble Frontier Fields lensing cluster A2744. We define three samples of star-forming galaxies: LBG galaxies with an LAE counterpart (92 galaxies), LBG galaxies without an LAE counterpart (408 galaxies), and LAE galaxies without an LBG counterpart (46 galaxies). All these galaxies are intrinsically faint because of the lensing nature of the sample (M1500 ≥ −20.5). The fraction of LAEs among all selected star-forming galaxies increases with redshift up to z ∼ 6 and decreases for higher redshifts, in agreement with previous findings. The evolution of LAE/LBG populations with UV magnitude and Lyα luminosity shows that the LAE selection is able to identify intrinsically UV faint galaxies with M1500 ≥ −15 that are typically missed in the deepest lensing photometric surveys. The LBG population seems to fairly represent the total population of star-forming galaxies down to M1500 ∼ −15. Galaxies with M1500 < −17 tend to have SFRLyα < SFRuv, whereas the opposite trend is observed within our sample for faint galaxies with M1500 > −17, including galaxies only detected by their Lyα emission, with a large scatter. These trends, previously observed in other samples of star-forming galaxies at high-z, are seen here for very faint M1500 ∼ −15 galaxies; that is, much fainter than in previous studies. The present results show no clear evidence for an intrinsic difference between the properties of the two populations selected as LBG and/or LAE. The observed trends could be explained by a combination of several phenomena, like the existence of different star-formation regimes, the dust content, the relative distribution and morphology of dust and stars, or the stellar populations.