Two-piece toilets have a separate tank and bowl bolted together. One-piece toilets fuse the tank and bowl into a single unit. The flush mechanism inside is identical. The difference is external: appearance, cleaning, weight, and price. Two-piece outsells one-piece by a wide margin because it costs less and is easier to move. One-piece looks sleeker and is easier to clean. Neither design flushes better than the other -- that depends on the internal mechanism, not the exterior shape.