Servers, VPS and VDS servers are related to hosting services but have different features:
Server: A server is a physical computer system constructed to deliver one or several services to users. It could be a simple dedicated server, in which case the whole physical apparatus is preempted by one particular client or it could a shared server wherein a number of clients use the same physical apparatus and its resources.
VPS (Virtual Private Server): VPS is still a server. The difference, however, is that VPS is a Server that is built rather on or in a host server. This offers all clients some of the resources run by, for example, one physical server (CPU, RAM, Storage, etc.) but keeps them separate from other local clients or users of that same physical server. Therefore, each VPS acts as if it were a dedicated server, as users are free to upload their operating system and applications.
VDS (Virtual Dedicated Server): A VDS is as well a virtualized server environment but like a VPS, the term is not as much deployed. There may be a specific use or a specific type of structure that might be referred to as a virtual dedicated server. Accordingly to the general understanding, VDS makes implication that the virtual server instance is provisioned with its own distinctive pool of resources without encroachment from external user or resources.
To summarize, even though they all fall under server hosting, the three terms cannot be used interchangeably. A server may connote both physical and virtualized environment while VPS and VDS purposely relate to resource possessed virtualized environment which is neither fully shared nor fully isolated.