This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
A servlet simply waits for an HTTP request and responds to it.
A Web Service request is a particular type of HTTP request, It is usually a post request that sends XML. The webservice (which can be a servlet) responds by sending some XML back. As long as the framework on each end understands the layout of the XML (SOAP, WSDL, etc..), Web Services can be used to allow programs on different machines, written in diffent languages, running on different platforms to communicate as if they were calling functions on a local machine.