Volition or will is the cognitive process by which an individual decides on and commits to a particular course of action. It is defined as purposive striving, and is one of the primary human psychological functions (the others being affection [affect or feeling], motivation [goals and expectations] and cognition [thinking]). Volitional processes can be applied consciously, and they can be automatized as habits over time. Most modern conceptions of volition address it as a process of action control that becomes automatized (see e.g., Heckhausen and Kuhl; Gollwitzer; Corno and Kanfer).
Willpower is the colloquial, and volition the scientific, term for the same state of the will; viz., an "elective preference". When we have "made up our minds" (as we say) to a thing, i. e., have a settled state of choice respecting it, that state is called an immanent volition; when we put forth any particular act of choice, that act is called an emanant, or executive, or imperative, volition. When an immanent, or settled state of, choice, is one which controls or governs a series of actions, we call that state a predominant volition; while we give the name of subordinate volitions to those particular acts of choice which carry into effect the object sought for by the governing or "predominant volition".
Within Gary Kielhofner's "Model of Human Occupation" volition is one of the three sub-systems that act on human behavior. Within this model volition considers a person's values, interests and beliefs about self-effiacy and personal capacity.
The book "A Bias for Action" by Heike Bruch and Sumantra Ghoshal discusses the difference between willpower and motivation. In doing so, the authors use the term volition as a synonym to willpower and describe briefly the theories of Narziss Ach and Kurt Lewin. While Lewin argues that motivation and volition are one and the same, the authors claim that Ach argues differently.
According to the authors, Ach claims that there is a certain threshold - when desire lies below this threshold, it is just motivation, whereas when desire crosses this threshold, it becomes volition. With this example, the authors point out the difference in commitment levels of individuals to tasks, by measuring it on the scale of intent - from motivation to volition. Modern writing on the role of volition in impulse control (e.g., Kuhl and Heckhausen) and in education (e.g., Corno) also makes this distinction. Corno's model ties volition to the processes of self-regulated learning.
Willpower is a concept that mistakenly assumes we are under rational control, and the reduction of the same results in a lack of willpower. The fact is that we turn our rationality to serve our impulses or wishes, and sometimes have great willpower in pursuing them. Thus an alcoholic can be very cunning in achieving his determination to drink, and may display great willpower in achieving this goal.
At other moments, he may rationally know that this behavior destroys his life, and costs him all that is dear to him, and may resolve for the moment to forgo it. That is when the observer deduces that willpower is a key to success, and with suffient will he would remain with that promise. However, at another moment another urge may become important, and he devotes his will and his rationality to satisfying that urge.
The observer's error is to assume that the human is a rational creature, and that will should serve that rationality. In fact, we are only partly rational, and often our rationality and determination serve various motivations that occur for causes other than reason.