From the FMCSA web site.
Class A: Any combination of vehicles which has a gross combination weight rating or gross combination weight of 11,794 kilograms or more (26,001 pounds or more) whichever is greater, inclusive of a towed unit(s) with a gross vehicle weight rating or gross vehicle weight of more than 4,536 kilograms (10,000 pounds) whichever is greater.
Class B: Any single vehicle which has a gross vehicle weight rating or gross vehicle weight of 11,794 or more kilograms (26,001 pounds or more), or any such vehicle towing a vehicle with a gross vehicle weight rating or gross vehicle weight that does not exceed 4,536 kilograms (10,000 pounds).
Class C: Any single vehicle, or combination of vehicles, that does not meet the definition of Class A or Class B, but is either designed to transport 16 or more passengers, including the driver, or is transporting material that has been designated as hazardous under 49 U.S.C. 5103 and is required to be placarded under subpart F of 49 CFR Part 172 or is transporting any quantity of a material listed as a select agent or toxin in 42 CFR Part 73.
The federal regulations seem to set the 10,000 pound limit on class B licenses issued for driving something like a 3 axle truck like a lumber delivery or dump truck, not a pickup. California seems to have set it's own standards judging by the previous post. No wonder there is so much confusion with the 10,000 limit varying from state to state.