Binding energy is an energy that is required to move an atom from the initial state to the final state releasing a photoelectron with a given kinetic energy. However, there is a potential difference that the photoelectron then experiences between the sample and being detected, so the recorded kinetic energy for a photoelectron is lower than the true binding energy. The work function is typically the name given to the energy required to calibrate the energy of a reference photoemission peak, such as Ag 3d5/2 so that the reference peak, as recorded appears at the energy expected for that peak on a binding energy scale. If you would like more information about work functions then a place to start is aip.scitation.org/doi/full/10.1063/5.0086359.