Research often operationalizes AI use in terms of frequency; however, frequency alone does not capture why or how students use AI. Drawing on help-seeking theory, we examined whether instrumental (learning-oriented) versus executive (task-completion) orientation toward AI differentiates students in ways that frequency does not, using a survey of 107 undergraduates. Academic self-efficacy mediated the academic engagement-AI literacy association, with cognitive engagement showing the strongest engagement-literacy link. AI use frequency was negatively associated with academic engagement; this relationship remained negative and was larger in magnitude when controlling for AI literacy. Instrumental users showed higher academic engagement than executive users, despite no difference in usage frequency. These findings suggest that whether AI is treated as a thinking partner or an answer source may be more meaningful than exposure frequency alone. Implications are discussed for how educators and course designers assess and support learning-oriented AI use, including distance and online learning contexts, where self-regulated AI use is particularly consequential.