Both are similar but I would say "energetic" is showing a high amount of energy/enthusiasm while active simply means doing things. For example active can be used in the sense of an "active lifestyle" to imply someone who does alot of sport or in general they have alot going on which means their life is "active"

Thank you so much!

Ffion had a great answer. Just to add onto that, "energetic" has to do with the amount of enthusiasm or energy you have which helps you stay "active", so active has more to do with your lifestyle whereas "energetic" has more to do with your current state or overall personality.