For one-way/ beam bending, stresses are determined the same. However, for beams, transverse stress is assumed zero, and for wide plates/ bars, transverse strain is assumed zero, which makes some difference in the vertical deflection.
For plates, it is much more common to have issues with large deflections where the plate begins to act as a catenary with tension in the plate in addition to bending. Generally, this means stresses are lower and deflections are smaller than predicted by bending alone. This also assumes the end supports can resist the applied tension, which can be very large.