On the one hand, you have filesharing-esque infringement. This is typically indicative either of social norms that are prohibited by DRM (e.g., loaning things you own to other people), or of demand in a market segment that the copyright owner is uninterested in providing (e.g., digital downloads, demo software). In either case, it is pretty strictly a matter of personal consumption and it often doesn't reflect a lost sale (and in many cases, it can create more sales later on).
The other kind is reflected in bootleg copies, or even outright plagiarism. In this case, the people making these copies are seeking to directly profit off of it (note that this isn't restricted to monetary profit), and they are doing so without any recompense or sometimes even acknowledgement to the original owner. It's fundamentally dishonest.
I see no issue with not calling the first kind of piracy theft but referring to the second kind as such.