The easiest way to differentiate Fish Crows from American Crows is by voice. Fish Crows have distinctive uh-uh calls, and also uh and eh calls, not heard from American Crows.
Both crows caw, but the Fish Crow caw is more guttural and sounds lower than that of the American Crow, even though the greatest intensity of the caws for both species is around 1.5 kHz. This is because the partials of the calls (the horizontal lines that stack to form the sound on the sonagram) are closer together in the Fish Crow, making the call seem lower to our ears. This phenomenon is nicely demonstrated on Nathan Pieplow's site Earbirding.
A flock of about 30 Fish Crows making various calls (Nov, NJ).
honk-like uh (center)
American Crow caw for comparison (Sep, ME).
The partials are stacked further apart, making the call sound higher.
In this recording of the same Fish Crow flock, presumed American Crow caws can be heard on several occasions in the background, including 6, 26, 39 and 64s.
The American Crow caws actually appear to be lower in pitch on the sonagram: