Turntable Output Grounds
It is safe to assume that for the audio signal, those two RCA shells are common. 

Where life can get interesting, especially with a mains-powered turntable and mains powered amplifier, is control of leakage currents at AC line frequencies, due to unintentional coupling of mains to ground through proximity capacitance, and intentional coupling of mains to ground through input filter devices.

To this end, most turntables and amplifiers are provided with a chassis earth screw connection on the back. This can be used to divert most of the leakage current to where you want it to flow, which is not in the shield of your audio coax cables. As turntables and amplifiers are not built to any given standard, you may need to experiment with connecting these chassis terminals, or not, to reduce any mains-related hum.