A web service will be running on a web server.
A web server is a piece of software designed to serve web pages/web sites/web services. Examples are IIS, Apache and many more. The name can also refer to the hardware running this software.
As web service will be running inside a web server – normally serving up XML or performing some action in response to input.
From wikipedia:
Web services today are frequently just Application Programming Interfaces (API) or web APIs that can be accessed over a network