✔ 最佳答案
자다 = sleep (verb)
잠 = sleep (noun)
=> 잠을 자다 = sleep (sentence fragment)
Therefore, there is no difference in the meaning between 잠을 자다 or 자다. They both means sleep.
Both sentences are gramatically wrong. They seem to have the same meaning of "Why does it matter whether to sleep or not?" "睡不睡有什麼相干/關係?"
But to express the phrase "to sleep or not", the conjunction "~가나 ~가나" or "~나 ~나" will not be used. There are at least 4 other forms that can be used.
So, if we ignore the irregularity in the form used, the 2 sentences have the same meaning and the only difference is the additional words "잠을" in the 2nd sentence.