Both cellular IP and mobile IP are open standards published by the Internet Engineering Task Force (IETF). The difference between the two is their zone of operation. Cellular IP is similar to a Local Area Network (LAN) whereas Mobile IP is analogous to a Wide Area Network (WAN).
Cellular IP was first proposed in January 2000, but has never been accepted as a formal standard. Mobile IP was defined in August 2002.
Another name for Mobile IP is IP-Mobility Management (IP-MM). One of its principal functions is to define a way to identify a point on the Internet that physically moves away from its addressed location. This issue is resolved by allowing a unit a second "care of" address, which enables an IP address to be patched to a different location. Cellular IP is a "micro-mobility" proposed protocol. This routes IP traffic within a fixed range over wireless devices.
Mobile IP is an officially endorsed international standard. Cellular IP competes with other micro-mobility solutions. A parallel with fixed wire routing is that the Border Gateway Protocol is mandatory for routing over the Internet, but a variety of routing protocols are available for LANs.