The term server can refer to either a computer dedicated to serving clients on the network, or a specialized application installed on that computer. Servers (usually) run operating systems that are configured to handle hundreds or even thousands of concurrent clients. A few examples of server operating systems include Windows Server 2016, FreeBSD, Solaris, Ubuntu Server, and Red Hat Enterprise. Server OSs often ship with default network services installed. They also make it easy to install additional network services, including resource-intensive applications such as email and database servers.
From a vulnerability scanning perspective, there is no practical difference between a network service and a server service, since network services run on servers, and servers provide their services on a network. When testing your server services, you can start with a standard vulnerability scanner. If you have specialized services, you might need a tool configured for that service.