Technical term for Internet-like network?

A private network that is accessible only to the employees of an organisation is called an intranet.

Definition: http://www.dictionary.com/browse/intranet

a computer network with restricted access, as within a company, that uses software and protocols developed for the Internet.

The same definition would apply in the military context. The difference might be that an elevated level of security precautions is imposed on such a network.

Wide area Network or WAN.

From Wikipedia:

A wide area network (WAN) is a telecommunications network or computer network that extends over a large geographical distance. Wide area networks are often established with leased telecommunication circuits.

Business, education and government entities use wide area networks to relay data among staff, students, clients, buyers, and suppliers from various geographical locations. In essence, this mode of telecommunication allows a business to effectively carry out its daily function regardless of location. The Internet may be considered a WAN.

An internet is any TCP/IP network. When used within a single organisation, it is called an intranet. The Internet is simply the public TCP/IP network that hosts the World Wide Web.