Migration certificate is issued by the board from where you have completed you class12th. Since this time you are changing your board/university so it is required. It allows you to take admission in any board/university. You can ask for this from the school where you have completed your class 12th.

Domicile certificate certifies that you belong to a particular geographic location. On a simple note, it provides information about your state. As many universities have state quotas so this is to ensure that they maintain the required ratios.