A Student/Child Account is a simplified, neuro-inclusive interface designed for your child to listen and follow along, focusing purely on the book without distracting "app" features. Your child may have already been given access to a Student account via their school.
A Parent Account is the "control center" where you can record stories, manage your kids reading and manage your family settings if you have multiple kids. If you don't yet have a Parent account, you can set one up by tapping the Settings button on any book, and then choosing "Parents Section".