There is a subtle difference between being tired and being fatigued.
I can't remember exactly where the reference is stated, but the Medical profession and the UK CAA recognise it as follows:
When you are tired, you are able to recognise and react to a given situation.
When you are fatigued, you are often unable to recognise and nearly always unable to react to the same situation.
Given the hours that pilots have to put in before and during a long haul flight, it would be interesting to know who would admit to being "tired" and "fatigued".