Quick Answer: NO, even-though they are both applications with different purpose.
Longer Answer: A web application is generally used to build websites which have UI (web pages, views, some presentation layer).
A web service is an application that provides services to consumers (web applications, thick clients, other services, mobile apps, etc.). Those services may provide data, perform some calculation or just about anything other than providing a UI. Thus, it will have a clearly-defined API which consists of providing responses to HTTP GET and POST requests made by a remote application. Now, this doesn't mean you can't access a web service from your browser, but it means that the application won't necessarily have a GUI user interface. For example: receive all results of GET and POST requests as strings of XML/JSON, which requires a client-side parser.