Failure vs. Exhaustion
Failure, Exhaustion, Fatigue are all similiar whether they are mental or physical. What we demand from our bodies may not be what we expect the outcome to be!
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To failure usually implies the amount of reps in a ladder form. Doing as many as possible with a given weight, then lowering the weight and pumping out more, and continuing until there is no juice left.
Exhaustion is different because it has to be reached through a higher weight or with an advanced form of rep.
As an example, HRT is done with exhaustion- specifically in the eccentric phase of the lift.
Pushing the weight in concentric phase then lowering in the eccentric phase for a 5 count forces the muscles to activate in a way that the body is not used to and is forced to compensate for.