On the topic of dedicated hosting, many web hosting services also offer managed hosting. This type of hosting sees the web host act as your IT department, handling a server's maintenance and upkeep. This hosting option is something that you'd typically find with dedicated servers, so it's a business-centric addition. Naturally, it adds a few bucks to the hosting cost, but nothing that should break the bank if you have the resources for a dedicated server.
Partitioning a single server to appear as multiple servers has been increasingly common on microcomputers since the launch of VMware ESX Server in 2001. The physical server typically runs a hypervisor which is tasked with creating, releasing, and managing the resources of "guest" operating systems, or virtual machines. These guest operating systems are allocated a share of resources of the physical server, typically in a manner in which the guest is not aware of any other physical resources save for those allocated to it by the hypervisor. As a VPS runs its own copy of its operating system, customers have superuser-level access to that operating system instance, and can install almost any software that runs on the OS; however, due to the number of virtualization clients typically running on a single machine, a VPS generally has limited processor time, RAM, and disk space.
A VPS runs its own copy of an operating system (OS), and customers may have superuser-level access to that operating system instance, so they can install almost any software that runs on that OS. For many purposes they are functionally equivalent to a dedicated physical server, and being software-defined, are able to be much more easily created and configured. They are priced much lower than an equivalent physical server. However, as they share the underlying physical hardware with other VPSes, performance may be lower, depending on the workload of any other executing virtual machines.