Beating and whisking eggs are similar but when you're beating the eggs you're just mixing the eggs up such as through using an egg beater or electric mixer to beat the eggs or other ingredients.
When you whisk eggs you are mixing the eggs but also incorporating air into the eggs.
When you're whisking the eggs you move the whisk around the bowl in a circular motion and twist your wrist while whisking.
While beating the eggs you would use an electric mixer to beat the eggs at a high speed and just move the mixer around in the bowl of eggs.
Whisking the eggs you just use a hand motion to spread the eggs around in the bowl.