Art & Worlds has two completely different pictures. Each ring's two faces are printed at different angles, so a ring that's upright on one side is crooked on the other.
Arcane Atelier is spot the difference. Both sides are almost the same picture and line up exactly, so flipping a ring shows the same spot with only the small differences changed. On Normal and Hard you have to find those differences to know which face you're looking at.
Classic. Solve one side. The Flip button starts a new scramble on the other side, and each side keeps its own best time.
Challenge. Solve one side and the disc turns itself over with every ring on the right face but crooked. The clock keeps running until both sides are restored.