The longer answer
The target is a shallow saucer-shaped disc made from a brittle mixture of pitch and ground limestone designed to shatter cleanly when struck and to biodegrade where it lands. The rim is usually painted bright orange so it reads well against grass and sky; the dome is dark so the underside flashes as the clay rotates through its arc.
You'll rarely hear it called "target" in conversation at the club. "Bird" is the dominant informal name — a holdover from the days when live pigeons were thrown — and "clay" runs a close second. "Clay pigeon" appears mostly in writing. Use whichever your range uses; they all mean the same disc.