Typically max refers to working with weights or some other form of resistance training. When we work against resistance, the recruitment of muscle fibers is type I, then IIa then IIb. Maximal effort suggests that we recruit to the IIb fibers. This is what is necessary for maximal power training. When we train to temporary muscle failure we have recruited into the IIb fibers. You haven’t missed any formula, just work to temporary failure.
A voluntary maximal action or maximal voluntary muscle fatigue is the maximum number of muscle contractions that can be achieved for a particular load using proper form and control. It implies that no extraordinary stimulation is used to produce further contractions of the target muscles. The idea is to work the muscles more safely, yet still achieve sufficient stimulus to produce a beneficial effect. The muscles tissue may have reached “failure” or may not. That is, if you were being coached (or given a sufficient encouraging stimulus), you might be able to continue using the muscle tissue for more contractions. But the risk of injury multiplies for each such forced contraction. And in almost every case of a forced contraction, proper form and control are no longer possible. Almost always setting the exerciser up for some level of injury. Depending on healing capacity, this could easily lead to chronic or more serious injury if the exerciser continually uses forced contractions when exercising.