Taillight - Generic term that could refer to any part of the assembly or the bulb. Context required. (i.e. "your taillight is cracked" = lens, "your taillight is out" = bulb, "insert the bulb into the rear of the taillight" = forward shell, etc.)
Taillight Assembly - The entire taillight, including the lens. Strictly speaking, this excludes bulbs. A manufacturer list component "taillight assembly" will not include bulbs when ordered. When on the car, however, many would refer to the bulbs as part of the assembly.
Taillight Lens - The transparent rear facing portion of the assembly.