To be specific, pickup selectors almost always run the pickups in parallel when both are used.
Though series is also possible with SPDT or DPDT center-off or SP3T/DPDT On-On-On switches.
If you want single coil options, you will need a rotary toggle switch with at least three poles, in order to shunt coils, in addition to pickup selection. It is also possible to do coil splitting when the pickups are soloed, using a DP3T/4PDT On-On-On switch.