Ah, the light dawns. What you are holding is an adapter that will take a standard C threaded head, like the Lumens Factory D36 Mini Turbo, and an E threaded body tube extension, with the goal of making a single cell E sized light with a C sized head. Gotcha.
In normal use, the unmodified phrase "E to C adapter" usually means an adapter that can be screwed onto a normal E sized body, to allow it to use a larger C sized head, like the afore mentioned D36 Mini Turbo Head, or any of the Surefire K series LED replacement heads that are C threaded.