Hello, Serkannn. The two sentences basically mean the same. We would almost always use the first sentence 'I want you to go' when writing, unless you were using reported speech in an article e.g. he said 'I want you going'. Orally, both phrases are correct but, again, the first sentence is most common. The second sentence is an abridged version, the real sentence being 'I want to see you going'. Perhaps, if we take an example where, say, your mother wants you to go to school and apply it to the two sentences. Sentence 1: I want you to go to school. (this is just a straight forward statement delivered most likely in normal monotone speech and is more of a request). Sentence 2: I want (to see) you going to school. (in this sentence the indication is that you have not been going to school and that your mother is annoyed. So the words 'I want you' are delivered in a higher more aggressive tone, so it is an order rather than a request. The phrase following 'going to school' would be in lower, normal speech.