A shared web hosting server, as the name implies, is a server that is shared by a number of web hosting clients.
A virtual private server (VPS), also known as a virtual dedicated server (VDS) is a server that is shared by multiple clients, similar to shared hosting, but each client gets their own virtual, or simulated, dedicated server facilitated by virtualization software. The virtualization software mimics a dedicated server environment allowing greater flexibility in the server configuration than a shared server.