Note: This is NOT a post about the book, Twilight, by Stephenie Meyer. Please continue on.
For Your Information
Twilight begins when the sun sets. It lasts until dusk, which is the end of twilight, or more specifically, when the sun is 6 degrees below the horizon.
So, twilight is a period of time, dusk is a certain moment.
Morning also has a twilight period, the time between dawn, the beginning of morning light, and the sunrise.
Just in case you were wondering. See here for more information.