CER II - You are confused about what your different lights are called and how they operate. Your DRLs are your headlights BUT ONLY WITH REDUCED INTENSITY. The lights in the bumper are FOG LIGHTS.
Attached is a .PDF copy of the 2002 Tundra Owner's Manual section pertaining to lights & wipers. On page 80 is a description of exactly how the DRLs and headlights function. On page 82 is a description of the fog light operation.
2002 Tundra Owner's Manual.pdf
If your truck doesn't operate as described in the Owner's Manual then somebody (previous owner?) has modified it somehow. As originally built, the FOG LIGHTS (when turned on with the dash mounted switch) will automatically shut off IF you turn on the headlight high beams. There are numerous posts here on TS about how to modify this to allow fog lights to operate as driving lights WITH the high beams on.
You can access the entire Tundra Owner's Manual for free by registering on the Toyota Owners website and entering the VIN of your truck.
You can also get all repairs/maintenance previously performed by any Toyota Dealer once registered.