We extend our previous studies aimed at modelling Lyman α emitters (LAEs) to the second population of high-redshift sources, Lyman-break galaxies (LBGs), with the final goal of investigating the physical relationship between them. We use a set of large (≈106 Mpc3) cosmological smoothed particle hydrodynamic simulations that include a detailed treatment of star formation, feedback, metal enrichment and supernova dust production; these same simulations have already been shown to successfully reproduce a large number of observed properties of LAEs. We identify LBGs as galaxies with an absolute ultraviolet (UV) magnitude MUV≤−17, consistent with current observational criteria. We then compute the evolution of their (a) UV luminosity function (LF), (b) UV spectral slope, β, (c) stellar mass function, (d) star formation rate (SFR) density, (e) (specific) star formation rate (sSFR), and compare them with available data in the redshift range 6 < z < 8. With no further parameter tuning, the model reproduces the redshift evolution of the LBG UV LF, stellar mass function and SFR density extremely well. It predicts a z-independent 〈β〉≈−2.2, in agreement with the most recently updated data sets at z≈ 6, but in slight tension with the steeper β−MUV observed at z≈ 7. The mean LBG sSFR increases from 6.7 Gyr−1 at z≈ 6 to 13.9 Gyr−1 at z≈ 8, and it is largest for the smallest (M* < 108.5 M⊙) LBGs, consistent with the recent findings of Schaerer & de Barros, and possibly resulting from a downsizing process. From a comparison of the simulated LAE and LBG populations, we find no appreciable differences between them in terms of the mass-weighted stellar masses/ages, SFR and dust content; only the faintest LBGs with MUV≥−18(−19) z≈ 6(8) do not show an observable Lyman α (Lyα) line. LAEs hence represent a luminous LBG subset, whose relative extent depends only on the adopted selection criteria. For example, using the Lyman α equivalent width selection threshold EW > 55 Å of Stark et al., the LAE fraction increases towards the faintest LBGs. However, for the canonical value of EW > 20 Å , all LBGs with −23 < MUV < −19 would be identified as LAEs at z≈ 6; the fraction of LBGs showing a Lyα line decreases with increasing redshift from z≈ 6 to 8 due to the combined effects of dust and reionization. We conclude with a brief critical model discussion, which emphasizes the uncertainties inherent in theoretical EW determinations.