Web is a form of client-server, with a HTTP Server and an HTTP client communicating back and forth.
Architectural differences between web and "traditional" database client server involve the use a different API and application layer protocol for communication, as well as a different server, for serving up data in a specific form instead of just serving up pages.
Other examples of client-server architecture would include:
* Email servers
* SNA/Gateway servers
* Middleware servers (JBOSS,TOMCAT, WEBSPHERE, ...)