Product design has always been a bad term. In the 90s I consulted with several companies who’s NPD based MEs were (and still are) called product designers while their in house industrial designers were called… industrial designers. UX/UI designers who are more focused on the actual core offering in a digital service have been called product designers since the mid 2000’s… basically the term product design stretched to sometimes mean anything from mechanical engineering, to industrial design, to digital interaction. The term product itself has been overly stretched. Go to your financial advisor and they will have plenty of financial products to sell you (stocks, bonds, and mutual funds).
I never understood some industrial designers aversion to the term industrial design. It is a much more defensible and unique tittle.