When you applied the term "dough" to cookie, and the term "batter" to cake, you supplied all the information you're going to get back. You see, when you include the terms "cookie" and "cake" you actually expand the possible definitions of "dough" and "batter." Darn it! Cookie dough and cake batter consistencies each cover quite broad ranges because there are so very many different kinds of cakes and cookies.
A "dough" usually includes a worked flour and shortening mixture somewhere along the line. It's usually something that can be handled. Doughs may be short (lots of shortening) or light, stiff (dry) or wet (sticky). These paramaters control the consistency which can range from very tough and dense and to ... At its most elastic definition you might say that the mixture of beaten egg whites with a pinch of flour that go to make meringues is a "cookie dough." On the other side of the spectrum, a good short-bread cookie dough is so short and stiff it melts on sight and crumbles when you breathe.
When you talk about cake "batter," the concept of "pour-able" is subsumed. But again, big range. Batters may be thick and smooth (cheesecake), creamy velvet (genoise), too light and fluffy too feel in the bowl (Pavlova), so thick it can't be stirred (fruit cake) or ... well, you name it.
Best answer: As a general rule, any dough is too stiff to be poured, and any batter too light to be kneaded. But there are exceptions to these rules, and consistency all depends on what kind of cake or cookie you're making. There is no generic right answer to the questions you asked. They're too general, and the subjects too broad.
Often questions like you ask are a preface to something more specific. Perhaps you attempted a specific cake, and it turned out badly; or you've got an assignment coming up for a cooking class and everyone else's mother bakes all the time but yours never does and you feel lost; or ... whatever. Please be as specific as possible and we'll see if we can't give you an answer that makes a difference.