By VPN, do people mean proxy?

VPN stands for “Virtual Private Network”. Back in the computer science classes at Uni, I learned to think about this concept, as if it’s a (seemingly) private local network. For example, suppose a company is based in London and New York. The company can connect all their computers in London to a private network. However, to make a computer in London talk to a computer in NY, the messages have to be sent through a public network, and thus VPN just provides an illusion that a network is private.

But I often hear people suggest using VPN to access a website that is blocked in my country. The way it works (in my understanding) is that my computer will forward a request to a server that has the ability to access the website, the server will talk on my behalf, and send the response back.

But isn’t this exactly a proxy? I.e.: my machine passes a request to a proxy server, which then forwards the request. Or does VPN technology work differently than how I understand it? If the VPN technology works as a proxy, why is it called VPN?

They mean using software that plugs into the operating system as if it were a VPN for the purpose of a proxy.

Could you clarify a few things, I’m trying to understand this precisely:

a) by “software that plugs into the OS”, do you mean a regular binary file that the OS can execute, or does the OS itself get modified?

b) “as if it were a VPN for the purpose of a proxy”, could you elaborate? Isn’t VPN just a set of IP endpoints, exchanging encrypted data, why does OS need to know whether the network it is in is a regular network, or a VPN?