Regulator = regulates the gas pressure (which ever gas u play with, CO2, HPA) input to your gun (which can also affect the firing velocity).
ASA = air source adapter
it's there to connect your air source (CO2/HPA tanks, 12g CO2 cartridges, etc) to your gun.
Some ASA has built in regulators.
ASA and regulator can be positioned differently depending on the gun you have. Typically, the ASA is at the bottom of the gun and the regulator on the drop foward or built into the fore grip of the gun