Coming from a slightly different angle,
I’ve always said sick, not tired. It's one of the reasons I reject the Chronic Fatigue syndrome framing. I didn’t go to my doctor after a 2 weeks nasty illness saying I’m really tired, even if some do, I went to him after I’d failed to recover as a 16 year old and still felt ill, including of course the weakness and fatiguability (but as you say on good days, you don’t have overwhelming sense of exhaustion if you are mild to moderate). At the immediate time, the most strong symptom had been neck pain /migraines, and i was diagnosed with a neck injury.
If we are using the term extreme fatigue for mild-moderate cases, the severe cases are also left with no language, so debilitating fatigue would be better as that allows a spectrum. It’s not necessarily a suitable term for more mild cases, for the reasons &patterns of illness described . As you get to very severe ME where people have crippling weakness AFFECTING SELF CARE and normal cognitive function, sensory sensitivity & pain, bordering on paralysis in all domains & being extremely unwell ON EXERTION, then the framing of “fatigue”, whether with the adjective extreme or not, is problematic because it is too weak/ reductionist/ benign. I therefore have a contrary view to the post above that says the focus on fatigue/ tiredness is coming *from* the severely affected - when the severely affected have particularly resisted a fatigue framing