The multi-scale and quantitative modelling of the mechanical properties of disordered materials remains an open challenge. Linking the scales requires an intense dialogue between physics and mechanics to keep track of the complexity of the mechanisms involved. This is what is achieved in this work, which compares amorphous solids' plastic behaviour based on two radically different descriptions: atomistic (discrete approach) and elastoplastic (continuous description). It is shown for the first time that the macroscale mechanical response, including its fluctuations, can be reproduced quantitatively. The local mechanical response of the elastoplastic model is calibrated for different length scales using an innovative method. This quantitative calibration allows establishing a length scale corresponding to the size of the plastic events (a key physical parameter of the models) and bringing out naturally specific uncalibrated properties. It further enables us to identify the impact of different models ingredients to develop comprehensive multi-scale modelling strategies.