IP address
An IP address serves two principal functions. It identifies the host, or more specifically its network interface, and it provides the location of the host in the network, and thus the capability of establishing a path to that host. Its role has been characterized as follows: "A name indicates what we seek. An address indicates where it is. A route indicates how to get there."
The header of each IP packet contains the IP address of the sending host, and that of the destination host.
Private IP
PIP in telecommunications and datacommunications stands for Private Internet Protocol or Private IP. PIP refers to connectivity into a private extranet network which by its design emulates the functioning of the Internet. Specifically, the Internet uses a routing protocol called border gateway protocol (BGP), as do most multiprotocol label switching (MPLS) networks. With this design, there is an ambiguity to the route that a packet can take while traversing the network. Wherein the Internet is a public offering, MPLS PIP networks are private. This lends a known, often used, and comfortable network design model for private implementation.