So \"idempotence\" can be defined as:
An action, that if performed N times has the same effect as performing the action only once.
Got it, easy enough.
You're assuming idempotence means that the state of the server will be changed at most once by a series of invocations. Most of the time, people use this term to mean that the state on the server won't be changed at all by any number of invocations. Under these circumstances, the distinction between your two cases is immaterial.