IP address
An Internet Protocol address (IP address) is a numerical label assigned to each device connected to a computer network that uses the Internet Protocol for communication.
An IP address serves two principal functions: host or network interface identification and location addressing.
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.