For both the quantum and classical systems, we begin from the POSITION of the entity under study (wave function in case of quantum mechanics which indeed is a probability of finding where exactly the particle lies) which is a basic starting point and one cannot further reduce this to any other fundamental property.
Operators on wave functions or formulating the nature of this position with time can lead us to know the other physical properties of the system like velocity, energy etc.Just knowing the position or wave function, we can generate the rest of the information of the system.
This is not the case in electromagnetism.Electromagnetism is the interdependence of electricity and magnetism.Their existence is mutual.Here the basic unit is current which itself is a vector.Hence its starting point CAN BE further reduced to a more fundamental concept.Thus, its not an ab-initio model.