In my country there's a difference... a Product Designer is someone who designs a tangible product, selects the material, and makes simulations for resistance and stuff, perhaps a little coding if necessary.
UX/UI designer are the "same" they do the design of an app or website, but only the design and pretty much every UX designer doesn't know anything about User Experience, good practices nor trendings on web and apps.
Interaction Designer we don't have much of that kind of designer but are the ones that focuses, I think, in the merge of a product designer or hardware with the UX designer.