internet or Internet

'internet' (with a lower-case 'i') : any set of networks interconnected using the Internet Protocol Suite (TCP/IP)

The Internet (with an upper-case 'I'), or sometimes 'the open, public Internet' : the largest set of networks interconnected using the Internet Protocol Suite.

Intranet, Extranet

 

From a technical perspective, the term Internet refers to a particular collection of computer networks which are inter-connected by means of a particular set of protocols usefully called 'the Internet Protocol Suite', but which is frequently referred to using the names of the two central protocols, 'TCP/IP'.

The term 'internet' (with a lower-case 'i') refers to any set of networks interconnected using the Internet Protocol Suite. Many networks exist within companies, and indeed within people's homes, which are internets, and which may or may not have a connection with any other network. The Internet (with an upper-case 'I'), or sometimes 'the open, public Internet', is used to refer to the largest set of networks interconnected using the Internet Protocol Suite.

Additional terms that are in common use are Intranet, which is correctly used to refer to a set of networks that are internal to a single organisation, and that are interconnected using the Internet Protocol Suite (although it is sometimes used more loosely, to refer to an organisation's internal networks, irrespective of the protocols used). An Extranet is a set of networks within a group of partnered organisations, that are interconnected using the Internet Protocol Suite.
http://www.anu.edu.au/people/Roger.Clarke/II/OzI04.html