2-Dimensional metal Halide Perovskites (2D-HP) are at the limelight for their potential exploitation in light-emission related applications. In particular, the most-investigated <001<-terminated 2D HP family shows dominant narrow light emission, with reduced Stokes shift, of great interest for display applications. In parallel, these systems often show additional largely Stokes-shifted emission, with reduced spectral resolution, of interest for the lighting application, e.g. development of white light-emitting diodes. Clarifying the emission mechanisms in 2D-HP and explaining the coexistence of these two contrasting emission regimes is greatly coveted, for the further exploitation of this class of semiconductors. Here, Density Functional Theory (DFT) simulations estimate total electron-phonon interaction in 2DHP in the order of few tens of meV, in agreement with ps-resolved UV-vis measurements, consistent with the reported narrow emission. On the other hand, such small coupling significantly contrasts with the assignment of broadband emission to some form of intrinsic (defect-free) self-trapped exciton. Additional DFT simulations rather assign broadband emission to extrinsic self-trapping, associated to point defects, halide interstitials in particular. This result is in line with similar findings for the parental 3D halide perovskite and highlights, on the one hand, the role of halide defects in lead-halide perovskitoids frames, and explains, on the other hand, the apparent contrasting nature of narrow and broadband emission, as due to two different emission mechanisms. Defect engineering protocol are therefore suggested, to optimize broadband emission in 2D-HP materials.