The ARRL actually has an FAQ that discusses this topic explicitly:
ARES is activated before, during and after an emergency. Generally, ARES handles all emergency messages, including those between government emergency management officials. RACES, on the other hand, almost never starts before an emergency and is active only during the emergency and during the immediate aftermath if government emergency management offices need communications support. RACES is normally shut down shortly after the emergency has cleared.
The FAQ continues into more detail, but the general gist is that RACES is specifically for coordinating actual civil services, whereas ARES is a more general communications network for overall messaging around emergencies.