I sort of think piracy in this context is actually distributing some media, e.g. a movie, without holding the copyright or a license from the copyright holder t

I sort of think piracy in this context is actually distributing some media, e.g. a movie, without holding the copyright or a license from the copyright holder to do so. You will argue that this may deprive the copyright holder of some rent if the media is for sale, but that sounds qualitatively different than taking or stealing.