DOT is actually for more than just lights or tires....it is the "Department Of Transportation". (DOT approved means that it is approved for on-highway/road use.)
CARB- is the California Air Resources Board. (They are an organization that regulates the EMISSIONS of vehicles, or parts for vehicles that could possibly affect the emissions of a vehicle. But that is a California thing.)
You should alwayz check your LOCAL laws if you have questions, because the laws vary greatly from state to state, and CA has some of the most strict laws in the country when it comes to vehicles.
This I know for a fact. (having to deal with these exact types of situations, and CHP....[modified exhaust, window tint, lighting, lack of mud flaps with oversized tires, open element air filter, hot air pickup tube missing, timing advanced too much, etc......] with my other vehicle.)
ummmmmmmm, do I have to write something?