Simple answer: the latter sentence is wrong, as it lacks the do. Your first sentence is the correct one. Think of it as follows: the question why often or usually requires a doing or being verb form after it, such as does(singular)/do(plural). Why DO I answer this question/ why do you ask the question? Or, why is the sky blue? The why still requires a verb after it. Why is a doing kind of question - it is not asking about location, or time, or process. It is asking why people do or are whatever it is they do or are. Why are they so angry? Please note you have missed out an IS after what in your question as well, in a similar mistake. The what here requires an IS after it in this case. So: what is the difference between...

As a question, the second sentence is wrong. The structure tells me that it's a statement.