Physical reservoir computing has emerged as one of the cutting-edge directions for designing efficient and low-cost neuromorphic computing systems due to its elimination of complex matrix calculations. Currently, the key challenge hindering its development lies in achieving adaptive control of complex computational tasks within a single physical reservoir layer architecture. This study constructs a physical reservoir computing system based on radial magnetic vortex nano-oscillators and investigates the relaxation characteristics of current-modulated magnetic vortex core dynamics. Two benchmark tasks, handwritten digit recognition and chaotic time series prediction, are demonstrated using the proposed magnetic vortex physical reservoir computing system architecture. Furthermore, the relationships between the relaxation time (τ) of the magnetic vortex core, the information processing capacity (IPC) of the physical reservoir layer, and the computational performance across different reservoir computing tasks are explored. The results indicate that the computational performance of handwritten digit recognition task exhibits strong positive correlation (0.92) with the nonlinear component of the IPC, primarily influenced by the rapid relaxation behavior of magnetic vortex core radius under high driving currents. Large-current-driven magnetic vortex core dynamics can achieve handwritten digit recognition accuracy up to 97.8%. In contrast, the chaotic time series prediction task demonstrates strong negative correlation (-0.87) between computational performance and the linear component of the IPC, mainly affected by the slow relaxation behavior of magnetic vortex core radius driven under low driving currents. The optimized magnetic vortex core dynamics within small currents can attain normalized mean square error (NMSE) as low as 0.06 in the chaotic time series prediction tasks. These results not only establish connections between the reservoir computing performance for different benchmark tasks and typical physical parameters such as relaxation time and IPC, but also enable adaptive switching between different tasks based on current-controlled radial magnetic vortex core dynamics. This work provides an important reference for hardware optimization and multi-task applications in adaptive physical reservoir computing systems.