The apprentice could learn unique jutsu from Orochimaru. Since Orochimaru is known for his forbidden jutsu, the apprentice might gain an edge in combat but also face the danger of being corrupted by the power. They could then use these skills in battles against common enemies. And, in the process, they might try to redeem Orochimaru in some way, like showing him that there is a better path than his thirst for power.
Naruto would likely become more secretive. Since Orochimaru is a very private and often devious character, Naruto might pick up some of those traits. He would probably keep things from his friends more often.
They would develop in terms of their skills. Under Orochimaru, they would gain a lot of knowledge about chakra manipulation and forbidden jutsu. But with Naruto, they would learn about the power of bonds and friendship. This combination could lead to the development of new jutsu that combines both physical power and the strength of relationships. Also, they would grow in their understanding of right and wrong, as Naruto's moral compass would constantly be in conflict with Orochimaru's more amoral stance.
Naruto's character would likely be darker. Orochimaru is known for his unethical experiments and thirst for power. Naruto, under his tutelage, might be more focused on individual strength rather than the bonds he values in the original series. He could become more secretive and less trusting of others.
In fanfiction, if Naruto were Orochimaru's son, he would likely have access to different types of jutsu from the start. Orochimaru is known for his vast knowledge of forbidden jutsu. Naruto could inherit some of that knowledge or even some of Orochimaru's unique abilities. His training would be radically different, perhaps more focused on experimentation and the pursuit of immortality like Orochimaru. This would also put him at odds with many of the traditional ninja values in the Hidden Leaf Village.
He might learn Orochimaru's signature snake - related jutsu, like the Hidden Shadow Snake Hands. This jutsu allows the user to summon snakes from their sleeves or other hiding places to attack opponents.
In some fanfictions, Naruto might go to Orochimaru seeking power. He could be tempted by Orochimaru's knowledge of jutsu. Maybe he thinks that by learning from Orochimaru, he can become stronger faster and be better able to protect his friends and the village.
In fanfiction, if Naruto were trained by Orochimaru, he might gain some very dark and powerful jutsu. Orochimaru is known for his unethical experiments and forbidden jutsu. Naruto could become a more morally ambiguous character, as Orochimaru's influence might taint his usually positive and straightforward nature. His power level would likely skyrocket, but at the cost of his relationships with his friends in Konoha who might be wary of his new, darker abilities.
In a fanfiction where Naruto is adopted by Orochimaru, Naruto's development would take a very different turn. Orochimaru could train Naruto to be more ruthless in combat. However, Naruto might also resist Orochimaru's darker intentions. This internal struggle could be a major part of the story. Naruto might try to find a way to use Orochimaru's knowledge for good, while still holding onto his own values. He could also face discrimination from other ninjas who see him as Orochimaru's apprentice and therefore a potential threat.
Well, Naruto could potentially be used as a bargaining chip by Orochimaru. Orochimaru might try to trade Naruto for something he wants from Konoha, like secret jutsu scrolls or some kind of political power within the village. And Naruto, being the determined hero he is, would likely be constantly looking for a way to escape and foil Orochimaru's plans.
If Naruto were to join Orochimaru in fanfiction, it would be a huge deviation from the original story. Naruto's values of loyalty and friendship would be put to the test. He might start to see the world from Orochimaru's perspective, which is often self - serving. This could also mean that Naruto would be involved in Orochimaru's plans to gain immortality, perhaps even becoming a part of his body - swapping experiments in some extreme cases.