Well, one way could be in their physical abilities. Maybe in the fanfic, Naruto is shown to have some of Zetsu's stealthy movement skills, like being able to blend into the environment in a similar way. Another similarity could be in their connection to nature. Zetsu has a strong link to the plant - like aspects of nature, and Naruto's chakra might be shown to have a similar kind of connection in the fanfic.
I'm not sure specifically as there could be many different interpretations in fanfiction. But it might involve Zetsu using his unique abilities to rescue Naruto from a dangerous situation, like a powerful enemy attack or a life - threatening trap.
A third theme could be growth. They both start from certain points in their characters and develop over the course of the fanfic. Tobi might become more serious or Zetsu might open up more, depending on the plot and how the author wants to develop their relationship.
One main theme is loyalty. Given their relationship in the Naruto series, fanfictions often explore how loyal they are to each other and their common goals.
In a fanfic where Naruto is trained by Zetsu, the story could take an interesting turn. Zetsu has knowledge of the Akatsuki and their secrets. Naruto could learn about the organization from the inside out. This knowledge could help him in his quest to bring peace. He might also gain some physical enhancements. Zetsu is quite durable in his own way, and Naruto could inherit some of that sturdiness. This would make him an even more formidable opponent in battles against strong foes like Pain or Madara.
One idea could be a zetsu crossover with Naruto characters in a different timeline. For example, Zetsu interacting with a younger version of the Sannin. Another could be a crossover with characters from other anime like One Piece, where Zetsu might find himself on the Grand Line. Or a crossover with characters from a fantasy game world, and Zetsu has to adapt to the new magic system there.
One common theme could be forbidden love. Since Zetsu has his own nature in the Naruto world and Sakura is a shinobi, their relationship might be seen as something that goes against the norms. Another theme could be the exploration of their different powers in relation to each other. For example, how Sakura's medical ninjutsu could interact with Zetsu's unique abilities.
One interesting sakura and zetsu fanfiction could be about them teaming up on a mission in a different dimension. They might face new and strange enemies, and through their combined efforts, they learn to understand each other better.
One good Sakura and Zetsu fanfic could be 'The Unlikely Alliance'. In this story, Sakura might find herself in a situation where she has to team up with Zetsu for a common goal. Maybe they are in a strange land and need to rely on each other's skills. Sakura's medical ninjutsu could come in handy when Zetsu gets injured, and Zetsu's knowledge of the area could help them navigate through difficulties.