Orange daylily: "Look, orange lilies!" That's what most people would call the Hemerocallis fulva, not knowing its latin name. Therefore, it is commonly called the ditch lily.
Common daylily: Although it looks similar to a lily, the Hemerocallis fulva isn't actually a lily. Since each flower only blooms for one day, the plant is known as the daylily. This particular species is the most common in the genus, so this is why it is called the common daylily.