Ground vs Power Ground
In circumstances where there are a number of components that need to make a "0V" reference connection, it's best to group these together and call it a different name (not power ground) and make one single connection to power ground from this collection of components.

This prevents power_ground_currents causing small mV differences in the 0V reference because the current will not pass through the reference connections. Normally, the common link for the 0V reference supply and the power ground will be made close to the incoming power feed.

Sometimes the two "ground" connections can be isolated without interconnection but I can't see that this is the case with your device however, neither can I see anywhere in the data sheet that tells you how to definitively make the connection between the two.

The power ground will always be the noisier because it is likely passing much, much larger currents than what I refer to as the reference 0V.

It's more common to have this problem in audio amplifiers where the speaker return wire makes its return connection through the 0V on the input stage instead of heading right back to the battery or power 0V connection. The current that flows in the speaker creates small ac volt drops on the sensitive input circuits and suddenly the whole thing just oscillates instead of being stable!