Many people say at 2 years is considered to be Adult GSD and fully mature at 3+ years old. Some people say the fear period as puppy GSD ends at 18 Months of age, meaning he is qualify to be as self-confident GSD like an adult dog.
When you're talking maturity there are many factors involved. Bone freeze occurs around 11 months. There will be no more "growth" after that, but they will "fill out" until the age of 2 and some, beyond that. It has been my experience, when they are 3, they are mature mentally.
Dogs will consider puppies as just that until about the age of 6 months, then all bets are off. This is when you may start to see aggression from an older dog toward the youngster. Sometimes, it will be just to put them in their place, but it can lead to injury and even death.
Physically, 2...mentally 3...to another dog, 6 months