We present a study of the intersection between the populations of star forming galaxies (SFGs) selected as either Lyman break galaxies (LBGs) or Lyman-alpha emitters (LAEs) in the redshift range 2.9 - 6.7, 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 LAE counterpart (408 galaxies) and LAE galaxies without an LBG counterpart (46 galaxies). All these galaxies are intrinsically faint due to the lensing nature of the sample (Muv $ge$ -20.5). The fraction of LAEs among all selected SFGs increases with redshift up to z $sim$ 6 and decreases for higher redshifts. The evolution of LAE/LBG populations with UV magnitude and Lya luminosity shows that the LAE selection is able to identify intrinsically UV faint galaxies with Muv $ge$ -15 that are typically missed in the deepest lensing photometric surveys. The LBG population seems to fairly represent the total population of SFGs down to Muv$sim$-15. Galaxies with Muv$<-17$ tend to have SFRLya$<$SFRuv, whereas the opposite trend is observed within our sample for faint galaxies with Muv$>-17$, including galaxies only detected by their Lya emission, with a large scatter. These trends, previously observed in other samples of SFGs at high-$z$, are seen here for very faint Muv$sim -15$ galaxies, much fainter than in previous studies. There is no clear evidence, based on the present results, for an intrinsic difference on the properties of the two populations selected as LBG and/or LAE. The observed trends could be explained by a combination of several facts, like the existence of different star-formation regimes, the dust content, the relative distribution and morphology of dust and stars, or the stellar populations
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