From what we've been taught at networking lessons, I understand that a VPN (Virtual Private Network) is made to interconnect physically separate networks or computers via the Internet and sort-of emulate a local area network over these computers. I take applications like Hamachi, Tunngle or Evolve (RIP) as the main examples of a VPN.
Yet when I usually see a VPN mentioned, it is in sentences like "get a VPN to become anonymous" or "I am using VPN to hide my real IP address on this server". I fail to understand a) how could a VPN be utilized to connect to the Internet when it is made to interconnect private networks, and b) why is VPN used in such a manner when its purpose is different?
In these examples, people seem to be using a computer in the network as a medium in the transmission, masking the original IP address. Yet this usage matches another device I know - a proxy (Tor coming to my mind as one of the examples). But setting up a whole VPN seems pointless to me when all they need is a proxy server. Is it just me or do people really mix these terms up?