Fatigue to me is a legal term. Sleepy isn't. Fatigued means too tired to safely perform as an active duty crew member. We are all different, some have a higher threshold. That's why we have to have the legal framework for self-assessment. No manager or co-worker can tell me wether or not I'm fatigued, that's for me to decide.
And remember, we have to be fit until the last person has disembarked the aircraft that day. Until then anything goes. When you're coming in on your fifth day of getting up 3:45am and you have to go around because of a split flap with crap weather it's going to be tough going reading the QRH. And the authorities won't be there to hold your hand, they will ask you why you didn't divert to a longer field rather than land and go off the end. And the company will present 8 lawyers pointing at all the paragraphs in the company manuals stating why it's all your fault. Maybe you miscalculated the landing distance because your brain felt like regurgitated marshmallows, so what? You still did it.
Fatigue isn't just "am I too tired now?" it's "will I be fit enough to safely deal with the remainder of my day?"
Because you can bet your sweet posterior that IF you get an engine fire, an explosive decompression or a cabin fire that can't be controlled you will get it on day 5, after 3 hrs of sleep labouring with the equivalent IQ of a seagull. It will take you five minutes just to find the right checklist. Any company that pushes rosters that crew can barely sustain even with zero non-normal situations can be called many things but safety-minded isn't one of them. You're basically taking the chance that when something goes wrong it does so to a crew that isn't too tired to deal with it. They'll be tired alright, just hopefully not too tired.