In this paper, we present the relationship between privacy definitions for Radio Frequency Identification (RFID) authentication pro- tocols. The security model is necessary for ensuring security or privacy, but many researchers present different privacy concepts for RFID au- thentication and the technical relationship among them is unclear. We reconsider the zero-knowledge based privacy proposed by Deng et al. at ESORICS 2010 and show that this privacy is equivalent to indistin- guishability based privacy proposed by Juels and Weis. We also provide the implication and separation between these privacy definitions and the simulation based privacy proposed by Paise and Vaudenay at AsiaCCS 2008 based on the public verifiability of the communication message.