Private and Public Peering

Hi, Can someone tell me the difference between private and public peering? A peering paper I have read explained the switch is shared in the case of shared and non-shared in the case of private. I still do not understand. Appreciate if someone could shed some light on this matter for me. My guess is that public peering is done in a commerical internet exchange while private peering is done in a facility owned by either one of the ISP. Thanks, Hansen