Being a sportsman and a pilot, and having experienced what I would term fatigue & tiredness/sleepiness, I offer the following difference. To me, when I was sleepy it was difficult to think & concentrate and make clear decisions. When I was fatigued the same was true, but I include muscle tiredness and lethargy of movement.
I sure as hell knew I was tired, many times, in the seat. Adrenalin rose on the approach and then dissipated in the car park.
Coach drivers falling a sleep on long trans-Europe trips took years to be exposed. Tacho in the cabs to help combat potential tiredness of lorry drivers. In 80's we had company agreements about positioning taxi rides in the night. MAN - LTN in the middle of the night with a slumbering taxi driver at the end of their shift. All considered unsafe due to sleepiness. Us? No, we are TopGun stuff and big boys don't cry. This one size pits all is pure bollox. There in no buffer. When I was younger & fitter full o'beans I could handle a few night flights, a few earlies, a few jet-lagging long-haulers. In the latter years of my career (and remember we don't retire at 55 or 60 anymore) there is no way I could do more than 1 early and through the nights were a no-no. Every early & late shift you lose 1/2 nights sleep. 5 consecutive shifts is pure madness. On day 5 you are definitely sleep deprived. You get home for a few days off and just as your batteries are back fully charged and you are rested it's off again on the sleepiness merry go round.
I think the word 'fatigue' was introduced as a disincentive to use it. It is an extreme condition, difficult to quantify; very individual. It is where you are at the end of your limits. We are all different, but some muppet has made FRMS program and we are all supposed to fit in the box, neatly. It scares us to use the word, makes us feel inadequate. Well, if I haven't slept due to circumstances outside my control, e.g. hotel vacuum cleaners and slamming doors, neighbours dogs & BBQ's, and not to mention NYPD police sirens 24/7, then I consider I shall be fatigued by the end of the duty. If you phone crewing and say you are tired due lack of sleep it is logged as your fault. You have to use the word fatigued as defence. Even then a black mark goes in the book and you are one of the 2%.