From ICAO
Fatigue is defined as a physiological state of reduced mental or physical performance capability resulting from sleep loss or extended wakefulness, circadian phase, or workload (mental and/or physical activity) that can impair a crew member’s alertness and ability
to safely operate an aircraft or perform safety-related duties.
For all the tired vs fatigued people, the above definition from ICAO Fatigue Management Documents would suggest that if alertness is reduced for any of those reasons you are “Fatigued”.