Amherst have very distinct black markings over a light background and can be dyed many different bold, bright colors. Ring neck pheasants are brown with dark, wide uniform barring.
I already knew the difference but Google worked for me. A quick search turned up many clear images of the two.
If you are asking about application, the dyed Amherst are often used as accents in the collars/hackles of steelhead and salmon flies while ringneck is often used for bodies and tails on trout flies. However, you can use them whatever way you want. You're the boss.