What is Jack would only be asked in a few contexts. It would be asking for some information that could be answered with 'Jack is a ....'.
For example:
Peter is a dentist. What is Jack? Jack is a doctor.
I'm a sargeant. What is Jack? Jack is only a corporal.
Who is Jack is asking for more information to define who this person, Jack, is. Answers might be 'Jack is my brother', 'Jack is the man we met yesterday', 'Jack is the man in the blue suit' or 'Jack is the man who drives a Vauxhall Viva past our house at 3am every morning.'