U R correct, that both White Oak & Red Oak are families, with many different trees within them, but there is also a specific tree that is known as White Oak and a specific tree known as Red Oak.
Generally, Oaks with pointed leaf tips are in the Red Oak family (includes Black Oak) and leaves with rounded tips are in the White Oak family (includes Chestnut Oak). There are exceptions.
Generally, Oaks with pointed leaf tips are in the Red Oak family (includes Black Oak) and leaves with rounded tips are in the White Oak family (includes Chestnut Oak). There are exceptions.