Your supplier did not test that specific piece of material. They took a representative sample in one part of the entire heat. They probably took multiple but they have a standard place inside of the heat to be most representative of the whole. Depending on their heat size and casting method the chemistry can change throughout the heat. In a continuous cast situation you have a certain amount of mixing from one heat to the next that can change the chemistry.
Look at the uncertainty in your check standards. The supplier is using similar standards. That is the uncertainty just in the check standard. That does not take into account all of the other minor difference like surface prep, optic cleanliness, gas cleanliness, etc..
In the case of light elements like Carbon and nitrogen your supplier probably used a combustion method instead of an OES. I have used a spectromax with the UV optic and it did give useful carbon and nitrogen, much better than the older 90's era spectro's, however, the LECO was more stable and give more consistent results.
You should probably familiarize yourself with the product analysis section of the ASTM standard that you are ordering to. For example ASTM A480 in Table A1.1 lists the tolerance over the maximum for Carbon Between 0.010 and 0.030% as .005%. So, if you perform a product analysis the acceptable carbon maximum would be 0.035%.