I know the topic is as old as the barbell you have from your grandpa lying around the corner where your first hustler magazine is still waiting being read again.
I had a discussion with a friend of mine and gave him following explenation:
Failure: When you “fail” to complete your rep in full ROM with clean technique from the beginning to the end of the motion.
So if you lift a rep and its your 12 rpm,failure will occur if you try to lift a 13th rep.
If you just finish the set with this last possible (12th) rep-even it was damn tough and you squeezed it out,failure didn´t occured because you didn´t failed to compete the rep.simple enough.
Concentric failure:the point at which -cause of fatigue- you are stuck in the motion before you can fully complete a rep.
Isometric failure: When you still keep pushing the weight at the point of concentric failure (even when its not moving anymore) but then you have to lower it cause of the fatigue given.So you can´t hold it in that isometric position anymore.
Excentric failure: When you are not abel to lower the weight under controll anymore.
Do we go the same line or do you have better definitions than me?