Primary custody usually refers to the parent who has primary physical custody, i.e., the parent with the child spends the most time. In a joint legal custodial arrangement, sometimes a judge will delegate final decision-making authority to one parent, and that parent is usually the one with primary physical custody.
On the other hand, sole custody means that all the custodial rights-both legal and physical-are assigned to one parent and that the other parent has no rights. Having sole custody, however, does not alleviate the other parent of their obligations, such as child support.