A PPC is any PDA with a touch screen that runs a Microsoft operating system such as Windows Mobile 5/6 or PocketPC 2000/2002/2003.
A PPC phone is a PPC that is also a phone. It runs Windows Mobile Phone edition.
A smartphone is a phone that can run some PPC software. It lacks a touch screen, so smartphone software relies only on hardware buttons and is designed to be used with one hand. A PPC phone is first a PDA, then a phone. A smartphone is first a phone, then a PDA.