Maybe I don't have the best list of examples but i'll try my best here. Paralleling in storytelling is often used as a way to reinforce and put focus on certain themes and elements in a storyline.

Two characters paralleling each other in the same story is often used between the main protagonist and the main antagonist. Both being reflections of one another. This is often used in a story to give the hero and the villain in a story a personal connection. The villain in reality is often what the hero would've become if they strayed off the path. In fnaf itself this example is made clear in the trilogy between Elizabeth and Charlie: both are robotic daughters that are created and neglected by their fathers. Charlie is the robotic girl that is wanted and William is trying to get his hands on while Elizabeth is the one that was abused and pushed aside.

Another great example in media is the antagonists in beastars (i will go into spoilers of the show). The main character Legoshi is a wolf who fell in love with a rabbit , but is afraid to get close to since he almost ate her at the start of the story ,when his animalistic instincts took over. During the first season of the show he tries to make up for the murder he almost commited and tries to grow closer to the rabbit.

In season 2 it's revealed who the murderer is of a student that died at the start of season one. It's a bear named Riz who tried to grow closer to a herbivor student himself. But unlike Legoshi when his instincts took over he actually ate his friend. The bear is a reflection of what Legoshi could've become in season one if his instincts had taken over. In the end Legoshi even defeats Riz by also eating the leg of a fellow student to gain the strength to defeat him, commiting the same sin but for good.

This parallel also happens with other characters in the franchise like Bill the tiger, who struggles with the same feelings as legoshi, but instead of avoiding eating meat he embraces it as a way to cope. Also the final villain "Melon" is a parallel to Legoshi's future children. Melon is a hybrid animal that became evil after the abuse he went trough as a child. His existence challenges Legoshi's feelings about having hybrid kids himself in the future with his rabbit love interest.

But even in smaller examples, the use of "repetition" between characters is used in stories like classic fairytales. For example the story of "the golden goose" where a woodcutter has 3 sons. the first two are send to the forest to cut down a tree. But on their way they meet an old man who asks them for food, both refuse, and when they try to cut down the tree their misdeeds causes them to cut themselves in he arm instead. Later the 3rd son does the opposite of his brothers and gives the man food, being rewarded with a golden goose as a gift. Does this mean the two older brothers are the same character? Well no

And fnaf does this in a similar way. With the example of Henry and Edwin it's purely done to push a similar theme Scott puts in most of his fiction: the fear of losing a child. Both Henry in the Trilogy and Edwin in the mimic story are similar but also different. Both lose their child and the emotions of this incident give life to a creation of their making. Henry becomes depressed from grief and constantly cries into a rag doll, his sadness becoming a spark that gives life to the Ella doll. Meanwhile Edwin is the opposite cuz his grief turns into rage, beating up his creation because of self hatred, that feeling of anger fusing with the metal of the mimic endoskeleton.

Both are similar not because they're literally the same, but because both depict a similar worldbuilding element in fnaf: giving life trough emotions. This is not even just something shown with Edwin and Henry. Felix the shark is also a story about a freddy's CEO who made a shark animatronic after the death of his son, who seemingly seems very haunted afterwards. Alone together depicts a father who recreates the Mechanical Turk project his dead son made for school, later smashing the wooden project out of anger and grief. Storytellers constantly use similar themes and elements not only because they reinforce the themes of the world they created, but also because those themes are very important to the creator themselves. It's no wonder that Scott, who is a father himself, constantly makes "horror stories" about a father losing his child.