Ok, to be really clear:
BJS - Beijing City (city code, not an airport code)
PEK - Capital Airport (airport in Beijing)
NAY - Nanyuan Airport (airport in Beijing)
If you didn't have different codes for cities and airports you would make life difficult for most travel agents (and us airline folks as well) as you would have to check availability and schedules airport by airport in the CRS (Computer Reservation System). Now you can see all flights to that city, regardless of which airport, in one display. If you want flts to one specific apt only, you would just enter the code for that specific apt.