The photon count rate of superconducting single photon detectors made of MoSi films shaped as a 2 µm-wide strip and a 115 nm-wide meander stripline is studied experimentally as a function of the dc biasing current at different values of the perpendicular magnetic field. For the wide strip a crossover current Icross is observed, below which the photon count rate increases with increasing magnetic field and above which it decreases. This behavior contrasts with the narrow MoSi meander for which no crossover current is observed, thus suggesting different photon detection mechanisms in the wide and narrow strips. Namely, we argue that in the wide strip the absorbed photon destroys superconductivity locally via the vortex-antivortex mechanism for the emergence of resistance while in the narrow meander superconductivity is destroyed across the whole stripline, forming a hot belt. Accordingly, the different photon detection mechanisms associated with vortices and the hot belt stipulate the qualitative difference in the dependence of the photon count rate on the magnetic field.