The difference between the 2 grounds is what they are used for.
Signal ground provides a reference to which all signals in the device are compared against. Internal circuitry detects those levels and interprets them into useful values.
Chassis Ground is used more for shielding and grounding. The Shielding and Chassis ground on a cable are connected in a way to ensure that any external electric fields hava somewhere to go. By connecting one end to chassis ground external electric fields are conducted into the shield, then into the enclosure, then into the power supply ground and into the earth.
Only one end is connected to prevent ground loops which is another subject all together. The basic rule is that all errant electric fields are to only have one path to get to ground. Connecting both ends breaks that rule and creates a ground loop.
In some applications they are connected and others you want them isolated from each other as much as possible. It depends on how the equipment is being integrated and the power supply used.