When I first read your inquiry I didn't take in the second name very well and presumed it was another spelling of the Zug, Zuck, Zook name.I am so sorry and embarrased.
It just so happens that my sister married a ZUK.And I have been trying to get some grasp on the clan.All I have so far is that the name has been pared down and that the family's origins were from Russia. Their ZUK is pronounced as if it had an e on the end and would rhyme with Luke.
To answer your original question, are the names Zook and Zuk related? No.