I’m confused by the terms. When I make an PHP application that
1) can be called with an URL or HTTPRequest, with parameters (i.e. country id), and returns data (XML or anything else)
2) can be called in order to store data (i.e. user wants to store all his contacts online on the server)
Is that still ok to call this thing a “Web Service”, and the whole activity ranging from fetching data and submitting data a “Web Service Call”?
That’s absolutely a Web Service.
If you can think of your web service methods as analogous to API calls, you can call it a Web Service; cf. obligatory Wikipedia reference.