If we think the terminology, which I think is the main question here.
Web service refers to software, that serves data in any format (XML/JSON etc.) through some kind of web interface. That interface can be called API (Application Programming Interface). REST and SOAP are ways to design the API.
Application is the software that is using this API provided by the web service.
In the other words, web service is "server" and application is "client". Usually server serves machines and clients serve the user.
So in any way you choose to build your system, I would call the part that serves the data as "Web service" and the part that utilizes the data as "application" (or "web application" if such).
Sounds like in your case, you are building a web service that provides XML-formatted data for multiple applications. So my answer is: build the thing you are already building and call it web service.
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