The nonlinear Breit-Wheeler process is studied in the presence of strong and short laser pulses. We show that for a relativistically intense plane-wave laser field many features of the momentum distribution of the produced electron-positron pair like its extension, region of highest probability and carrier-envelope phase effects can be explained from the classical evolution of the created particles in the background field. To this end an intuitive semiclassical picture based on the local

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... t-crossed field approximation applied on the probability-amplitude level is established and compared with the standard approach used in QED-PIC codes. The main difference is the substructure of the spectrum, which results from interference effects between macroscopically separated formation regions. In order to compare the predictions of the semiclassical approach with exact calculations, a very fast numerical scheme is introduced. It renders the calculation of the fully differential spectrum on a grid which resolves all interference fringes feasible. Finally, the difference between classical and quantum absorption of laser four-momentum in the process is pointed out and the dominance of the former is proven. As a self-consistent treatment of the quantum absorption is not feasible within existing QED-PIC approaches, our results provide reliable error estimates relevant for regimes where the laser depletion due to a developing QED cascade becomes significant.