This study investigates how undergraduate students engage with ChatGPT in self directed learning contexts. Analyzing naturalistic interaction logs, we identify five dominant use categories of ChatGPT information seeking, content generation, language refinement, meta cognitive engagement, and conversational repair. Behavioral modeling reveals that structured, goal driven tasks like coding, multiple choice solving, and job application writing are strong predictors of continued use. Drawing on Self-Directed Learning (SDL) and the Uses and Gratifications Theory (UGT), we show how students actively manage ChatGPTs affordances and limitations through prompt adaptation, follow-ups, and emotional regulation. Rather than disengaging after breakdowns, students often persist through clarification and repair, treating the assistant as both tool and learning partner. We also offer design and policy recommendations to support transparent, responsive, and pedagogically grounded integration of generative AI in higher education.