'Fatigue' is a noun. I think you meant 'fatigued', which is an adjective like tired.
If I am fatigued, it is usually more intense than tired. I cannot function at all well when I am fatigued.
If I say a person is fatigued, or suffering from fatigue, I would probably get a picture of a person who is unable to do their work or anything else well.
It also refers to being mentally tired.
If I am tired, it tends to mean that I can still function, but could use a little rest. I just wouldn't do as well as if I was fully rested.
I can also use it to say that something has happened too much.
"I'm tired of your complaining." = I have had enough of your complaining.