CS1 shipping
CS1 requires the supplier to contain the suspect product and perform a redundant 100% inspection process. This process may be done by the supplier's employees, though some suppliers routinely employee an outside third-party inspection company to perform this service. Cost or availability of personnel is usually the driver for the decision whether to outsource this function or leave it in house.
CS2 shipping
The customer will require CS2 when the supplier has failed to correct the problem in CS1 or has had major quality problems. Each customer has their own criteria for placing a supplier in CS2, but normally it is used when the CS1 procedure has not corrected the problem.