Honestly, I had never seen these words before! But I looked them up in the dictionary, and this is the difference:
"Enculturation" is the process of learning your own group's culture, and "enculturate" is a transitive verb. So, when an American mother teaches her child to use a fork, she is enculturating him.
"Acculturation" is the process of taking on ANOTHER group's culture. "Acculturate" can be either transitive or intransitive. Used transitively: When an American moves to China, she might try to acculturate her child by teaching him to use chopsticks. Used intransitively: The child might naturally begin to acculturate by copying his Chinese friends.
Again, this is the first time I've seen these words. So if another native speaker sees any mistake, please correct me!