Does a web application have to live in a browser to be called a web application? Or is a thin client that uses a web service for most of it's functionality a web applicaiton?
From a layperson's perspective, I would say "yes". For my mother (as an example of a layperson who uses computers, but doesn't know much about them) using MS Outlook and using webservices through a thin client feels very similar. But, using a browser feels like "going online".
However, from a technical perspective and especially on the server side, there is very little real difference. So, from this perspective, I would say "no".
In the end, the answer depends on who you are talking to and what particular aspect of the application you are trying to emphasize. There is no single answer applicable in all situations.