Cognitive control and self-control are often used as interchangeable terms. Both terms refer to the ability to pursue long-term goals, but the types of controlled behavior that are typically associated with these terms differ, at least superficially. Cognitive control is observed in the control of attention and the overcoming of habitual responses, while self-control is observed in resistance to short-term impulses and temptations. Evidence from clinical studies and neuroimaging studies suggests that below these superficial differences, common control process (e.g., inhibition) might guide both types of controlled behavior. Here, we study this hypothesis in a behavioral experiment, which interlaced trials of a Simon task with trials of an intertemporal decision task. If cognitive control and self-control depend on a common control process, we expected conflict adaptation from Simon task trials to lead to increased self-control in the intertemporal decision trials. However, despite successful manipulations of conflict and conflict adaptation, we found no evidence for this hypothesis. We investigate a number of alternative explanations of this result and conclude that the differences between cognitive control and self-control are not superficial, but rather reflect differences at the process level.