Angeli and MacDonald reported a superlattice-imposed Dirac band in twisted bilayer molybdenum disulphide (tBL MoS₂) for small twist angles towards the R_h^M (parallel) stacking. Using a hierarchical set of theoretical methods, we show that the superlattices differ for twist angles with respect to metastable R_h^M (0°) and lowest-energy H_h^h (60°) configurations. When approaching R_h^M stacking, identical domains with opposite spatial orientation emerge. They form a honeycomb superlattice, yielding Dirac bands and a lateral spin texture distribution with opposite-spin-occupied K and K’ valleys. Small twist angles towards the H_h^h configuration (60°) generate H_h^h and H_h^X stacking domains of different relative energies and, hence, different spatial extensions. This imposes a symmetry break in the moiré cell, which opens a gap between the two top-valence bands, which become flat already for relatively small moiré cells. The superlattices impose electronic superstructures resembling graphene and hexagonal boron nitride into trivial semiconductor MoS₂.