Do LEDs have a wire filament?

No, LEDs operate using entirely different components. LEDs are diodes - they only allow power to move in one direction. The anode (+) is where the current comes in and the cathode (-) is where the current goes out, much like the positive and negative terminals of a battery. Incandescent bulbs project light in every direction (omni-directional) as opposed to LED lights which project light in specified directions (such as 20, 50 and 120 degrees) due to their package design and layout.