The main difference is what they can access when they log into the Parent Dashboard.
Primary parents have access to all features of the Parent Dashboard (enrolling campers; filling out forms; financials/making payments; etc.)
Divorced parents can only access the homepage, as well as Camp Today and Phone Call Scheduling (for camps who have purchased those modules).
From an admin's standpoint, both primary and divorced parents can be included on email communication, and both can be designated to receive the family's invoices (if they're on a payment schedule).