You might see carnitine listed as an ingredient in many "energy drinks," but that would be because carnitine itself acts as a fat metabolizer - it works differently than caffeine. Carnitine itself does not contain any caffeine, because it is a completely different molecule.
Nevertheless, people have still reported weight loss with carnitine and this is what it is mainly known for. Likewise, some will argue that caffeine can help burn fat if taken in small amounts before aerobic exercise (since it might keep you exercising longer than normal).
They share similar properties, perhaps, but otherwise caffeine and carnitine have nothing to do with each other.