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