While there can be many reasons and differences, the main reason is the federal government is just simply more generous with tax deductions and credits.  

For the Federal return, even being claimed as your dependent, your son would be allowed a standard deduction of $6,350 from income.  So, since he only earned $5844, this means he would not pay tax on any of his income and receive all his withholding back.  

For the same scenario (i.e. being claimed as a dependent), the state of Michigan only allows a $1,500 exemption from income.  So, this means your son must actually pay Michigan tax on a good portion of his income - hence, why he receives less of the withholding back.