Some may confuse VPS and VPN and may think they are similar or related, but in fact they have nothing really in common nor are they really comparable technologies. I think the most they have in common is literally the first two letters.
So what are they exactly?
VPS Stands for Virtual Private Server.
VPN stands for Virtual Private Network.
VPS - Virtual Private Server
A VPS is literally a server such as a Windows or Linux server, in fact the OS doesn't matter. It is a server that has access to CPU, RAM and Disk drives to process and server server resources such as web site. Virtual means that this server is not really a stand alone physical server that is sitting somewhere with CPU and RAM, but kind of. A VPS usually lives in a large physical server. This large physical server hosts many VPSes there by the many VPSes share the same resources as the underlying server resources. So if the main server has 3 GHz CPU and 10 VPSes are on the server then each has 10% of 3GHz CPU (over simplified). As far as the features, functionality and an end user is concerned the VPS behaves almost exactly like a regular physical server.
The benefits of VPS is that as you can image, it is cheaper than a full physical server. And because it is virtual or software based, it is easier to manage, backup, and event take snapshots of. In fact one of the most powerful features of VPS is that you can image them or make templates of them.
VPN - Virtual Private Network
A Virtual Private Network is not a server it is a Network. What is a network exactly though? A computer network is a technology that allows computers connected to a switch or router to talk to each other and send messages to each other. A virtual network means that it is not a physical network.
In a physical network, you would have at least two computers, say at the office, are connected to a physical switch. That's easy.
Let's say that a third computer sitting at home (on a different network) needs to communicate with the computers at the office. How is that possible. It's not because it's not connected to the same switch. But wait, with a technology called VPN, it is possible. You can install a VPN software on your home computer, provide it with a secret password and the information to connect to your office network and voila, your home computer will see be visible to the office computers. The technical details of how that happens is beyond the scope here. But essentially the computers all can start behaving as if they are on the same network.