Two-dimensional (2D) graphene has emerged as an excellent partner for solving the scarcity of ultraviolet photodetectors based on three-dimensional (3D) AlGaN, in which the design of a 2D graphene/3D AlGaN junction becomes crucial. This study investigates the response mechanisms of two distinct graphene/AlGaN (Gr-AlGaN) photodetectors in the lateral and vertical configurations. For the lateral Gr-AlGaN photodetector, photogenerated electrons drifting into p-type graphene channel induce negative photoconductivity and a persistent photoconductive effect, resulting in a high responsivity of $1.27\times {10}^4\mathrm{A}/\mathrm{W}$ and detectivity of $3.88\times {10}^{12}$ Jones. Although the response capability of a vertical Gr-AlGaN device is inferior to the lateral one, it shows significantly reduced dark current and self-powered detection. The photogenerated electron-hole pair can be spontaneously separated by the junction electric field and generate a photocurrent at zero bias. Hence, the vertical Gr-AlGaN photodetector array is satisfied for passive driving imaging like deep space detection. Conversely, the exceptional response of the lateral Gr-AlGaN device emphasizes its prospects for steady object recognition with low-light emission. Moreover, the improved imaging sharpness with light illumination duration makes it suitable for biomimetic visual learning, which follows a recognition to memory process. This study elucidates an efficient approach for diverse photodetection applications through the configuration design of Gr-AlGaN junctions.