Addressing the global caregiver shortage through socially assistive robots necessitates a deep understanding of their psychological and physiological impacts on older adults during human-robot interaction (HRI). This study addresses whether social robots can serve as effective interaction partners compared to humans, and if "positive prompts" can similarly enhance these interactions. We conducted a comparative study with 35 participants (aged 70+). Our multi-modal analysis, integrating facial expression data, heart rate variability, and subjective questionnaires, revealed no significant differences in overall stress levels between human and robot interactions. Facial expression analysis confirmed that the robot was accepted as a valid interaction partner, while physiological data showed slightly lower heart rates during robot interactions, suggesting a more relaxed state compared to human-led sessions. These findings indicate that social robots can engage older adults without inducing psychological strain and are capable of alleviating caregiver burden by performing structured tasks, such as health-sensing surveys. Future work should address the identified "appearance-content mismatch" in robot design to facilitate even more natural and effective interactions.