My car is a 2002. Is it subject to the California emissions standards?
If your car has less than 7,500 miles on the odometer and is a model year of 1996 or newer with a gross weight rating of 6,000lbs or less, yes, it is subject to the California emissions standards.
What about a light duty truck that fits that criteria? Is it exempt?
No, the criteria I listed above includes both passenger vehicles and light duty trucks.