Grounding question

I have a question about a schematic found in the files section, four
files down. It is called A Servo E-Stop Circuit.pdf.

There are two grounds mentioned in the schematic. One is on the AC
side and the other is on the DC side. The ground on the DC side is
part of a rapid discharge circuit for the capactor. When the E-stop
is hit, the relay goes to the NC position and discharges the
capactor. The question I have is, would the ground on the DC side
connect to the ground on the AC side?

I have a feeling it does not, but I want to make sure. I see the
circuit as starting at the + side of the cap and going to the
resistor, then going to the relay and then back to the -(GND)side of
the cap and stopping there. No connection to AC ground.

John