You might find Self Determination Theory interesting, which takes a detailed look the concept of motivation. Even if you don't explicitely mention it in your question, you seem to be refering to the difference between intrinsic and extrinsic motivation, which is a distinction that is traditionally made with respect to motivation.
In SDT this is taken a step further. Gagne & Deci (2005) introduce the distinction between autonomous and controlled motivation, which can be seen as two endpoints of a continuum. Intrinsic motivation is autonomous, and people who are intrinsically motivated engage in a certain behaviour because they like it, find it interesting, etc. In this sense, the behaviour is self-determined.
To the contrary, behaviour can also be externally controlled (e.g. your boss tells you to do something) and thus not self-determinded. In its most extreme form, this kind of controlled motivation is what we know as extrinsic motivation. However, a task that is extrinsically motivated can be internalized and thus become more autonomous and more important to the individual. Gagne & Deci postulate 3 degrees of Internalization, which vary from low to high. In its most internalized form, which is called integrated motivation, the behaviour has become autonomous and is equally important to the individual as intrinsically motivated behaviour, even though not for the same reasons.
In their article, Gagne & Deci (2005) make a couple of propositions derived from the theory, the first one of which also speaks to your question. Because integrated and intrinsic motivations differ in their underlying mechanisms, they should be predictice for performance on different kinds of task. An intrinsically motivated person should perform well on a task that she likes, whereas soemone with integrated motivation should perform well on tasks that require discipline and effort. This proposition has already been tested and confirmed with respect to political envolvement and voting behaviour (Koestner et al., 1996).
Gagné, M., & Deci, E. L. (2005). Self‐determination theory and work motivation. Journal of Organizational behavior, 26(4), 331-362. PDF
Koestner, R., Losier, G. F., Vallerand, R. J., & Carducci, D. (1996). Identified and introjected forms of political internalization: extending self-determination theory. Journal of Personality and Social Psychology, 70, 1025–1036.