Update Sept 2020 as these links have been way outdated (original post was in 2014!)
Web Requests shows ALL HTTP-based Web Requests dynaTrace picks up through Servlet, ASP.NET, Web Server and the Java & .NET Web Request Sensor Packs.
Web Services are those that are picked up specifically from our Web Service Sensor Packs, e.g: when your application uses AXIS to make a SOAP Web Service calls.
Check out the following two pages in the doc that give you more details on these two dashlets:
You can find all dashlet links here: https://www.dynatrace.com/support/doc/appmon/application-monitoring/appmon-client/dashlets/