I dislike the term "fatigue" about as much as the use of "malaise" in PEM.
On a good day, I would go along with the analogy "nothing left in the tank". My body feels starved of the fuel needed to be active.
On an average day, my muscles will start to ache about 10 seconds into an activity, such as cleaning my teeth. If I continue on, the muscles weaken and fail.
On a bad day, even lying motionless I am wracked with pain all over, I barely have enough energy to breathe, am nauseous, "fluey", light and sound sensitive. When this state drags on for weeks at a time, unremitting, I become scared that this is my new "normal" and I literally want to die.
Of the two choices given, I would say that disoriented state of getting up too early was closest, but only because of the fuzzy-headed, slightly nauseous feeling that can occur when woken up from a deep sleep. It does not encompass the " running on empty" aspect as the body works normally once it's up and out of bed, the head just needs a little extra time to "catch up" with the sudden and unexpected activity (hope that last line makes sense).