Final answer:
Central diabetes insipidus shows improved urine concentration after vasopressin administration, while nephrogenic diabetes insipidus shows no response to vasopressin.
Step-by-step explanation:
The difference between central and nephrogenic diabetes insipidus can be determined through a water deprivation test. In central diabetes insipidus, the urine concentration improves after the administration of vasopressin. On the other hand, in nephrogenic diabetes insipidus, there is no response to vasopressin, and the urine concentration does not improve.