I am not sure these explinations will be true all the time.
BUT- IMO

#1 "not approved by gaming"
Generally means the art work was turned down.
#2 "turned down by gaming"
Generally means the notched chip was turned down after the chips were made. In this case the distributor must destroy them without the casino ever seeing them.

The HR chip was turned down after the chips were made and a few days before the planned release date.

A chip sales recently told me gaming now requires an un-notched chip for final approval. I have not verified that yet, but it could put an end to NV notched chips, if true.