They are the same shrine. Aga Shrine is the official name, while Tarobogu is the popular name derived from Taro-bo, the tengu deity enshrined there.
The shrine specializes in prayers for victory, success in competitions and exams, business prosperity, and safe travels due to its association with Sarutahiko-no-Okami and the tengu deity Taro-bo.
The Aga Dengaku is performed during annual festivals, with the main performance typically in February. Check with the shrine office for exact dates as they vary yearly.
30 minutes to 1 hour is sufficient to visit the main hall, walk the grounds, and see the ancient cedar trees.
English signage is limited at Tarobogu Shrine, as it is primarily visited by domestic tourists. Bringing a translation app or researching the shrine beforehand is recommended for non-Japanese speakers.