Recent advances and applications of artificial intelligence (AI) have increased the opportunities for students to interact with AI in their learning tasks. Although various fields of scholarly research have investigated human-AI collaboration, the underlying processes of how students collaborate with AI in a student-AI teaming scenario have been scarcely investigated. To develop effective AI applications in education, it is necessary to understand differences in the student-AI interaction (SAI) process depending on students' characteristics. The present study attempts to fill this gap by exploring the differences in the SAI process amongst students with varying drawing proficiencies and attitudes towards AI in performing a public advertisement drawing task. Based on the empirical evidence obtained from the think-aloud protocols of 20 Korean undergraduate students, the study first conducted a lag sequential analysis to identify statistically significant linear patterns of each group and then chronologically incorporated them into the SAI duration via coded activity alignment series to distinguish the overall SAI process of each group. The study revealed the distinctive differences in SAI processes of students with different attitudes towards AI and drawing skills. To better facilitate student-AI teams for learning, a range of implications of educational AI development and instructional design is discussed.