The chip design seems to have had issues. From the data-sheet “To maximize the dynamic performance of the CM1803A, the analog and digital grounds are not connected internally. These grounds should have low impedance to avoid digital noise feeding back into the analog ground. Therefore, they should be connected directly to each other under the part to reduce potential noise problems.”
All depends on the chips and the circuit required. In some situations one would like to have a galvanic separation between the input from the computer and the output signals. This can be for safety reasons or to reduce interference. Take the AD5722, a DAC, it his logical and analog grounds. The chips internally is designed such that the input signal is galvanically separated from the output. (often an opto-coupler is used). They have done this so the logical input signal can be completely separated from the analog supply and output. If however you do not have a separation need and use only one power supply, then you connect the different grounds together, as they have done on the board and as such analog ground = digital ground and you can use it as the same.
