These are rechargeable lights. With the tail light, the actual light portion comes out of the silver shell and recharges with a USB cord. It seems to be a new-ish light called an "Aluma-lite", where the functional light unscrews from the little shell and you just charge with a phone charger or other USB cord. I should do a review, because it's actually pretty powerful for a tail light, and it looks better than most of the modern, rubber ones.
The front light is a light I made from an old Miller lamp shell - I mounted a cree LED in the light dish and soldered a swith for it. A rechargeable battery rests on the shelf of the lamp bracket.