When we think of training the core through functional movements, it means we’re targeting that muscle group in the way it is supposed to work to stabilize the body either from a standing position, pronated, supinated, and seated position. There are various functional exercises that hit the core with just the right intensity when performed with proper form. Exercises such as a pallof press challenges the core from an anti-movement point, stability plank circles work the core both linear and rotationally and these can be great examples of functional core work. Functional core exercises emphasize both endurance and strength.
Aesthetic core work involves more isolation of the muscle group while doing a fixed movement. Doing aesthetic core training emphasizes size and strength more. The exercises options vary on which specific parts you want to target. Ex: Seated Crunches, Leg raises, Decline crunches, side planks.
As an athlete, functional core training is more beneficial because it simulates the way we move throughout performance. A weak core will increase the injuries to lower backs due to lack of core muscular endurance.