web service

The web2 and service-oriented architecture standards all use the term web service and never use the deprecated term website.

The terms web application and webservice are used by Wikipedia, which has an article on web 2.0 that acknowledges the changing terms, and distinguishes user interfaces or applications from behind-the scenes services. It's not clear if those terms will catch on. Eventually the GFDL corpus namespace will probably reflect the dominant usage that emerges. In the meantime a web service can be either or both.

[+] living ontology prefers just "web"

advanced services

Advanced web services such as those from Amazon are usually called "web services", and this is the usage that has become standard, e.g. at OASIS, W3. As of 2006-03, up to three quarters of UK firms were failing to make transactional use of the net - possibly, the static 'site' metaphor was preventing it.

[+] the dying "website" or "web site" metaphor