Both VPS servers and cloud servers have several similar features and are based on virtualization. The basic difference is that VPS servers are created by splitting a powerful physical dedicated server into several smaller virtual servers. Each of the VPS works as a dedicated server Cloud servers are a big network of machines that are connected together and made available to the users on rent. Cloud follows the pay-as-you-go model while VPS hosts charge a flat monthly rent.
Cloud offers higher availability at times of a server failure, your business is shifted to other servers but in VPS, if the server or any component fails your server will be down till such time the physical server is attended to. In cloud you get complete dedicated resources but in a VPS server you get a portion of the server resources like space and bandwidth while the CPU and memory are shared. VPS providers may offer only one operating system while in cloud you have a choice.