ArcGIS Enterprise gives you complete control over your deployment. It can be run on a single server machine, or scaled across many machines
ArcGIS Server is software that makes your geographic information available to others in your organization and optionally anyone with an Internet connection. This is accomplished through web services, which allow a powerful server computer to receive and process requests for information sent by other devices. ArcGIS Server opens your GIS to tablets, smartphones, laptops, desktop workstations, and any other devices that can connect to web services.
At IGCMC we use ArcGIS Server as it allows us to expose our GIS as a set of web services. Web services are software code or components that run on a specialized machine called a server. Web services receive requests from other apps and machines, called clients. The request might be to send some information or process some data. GIS web services do things related to sending and processing geographic information.