Can you put turtles in the same cage together if one is bigger than the other turtle?

yes, you can. i have a very large turtle and a smaller turtle in the same tank and they get along fine. if you see the large one chasing the other, it may have food in its mouth so feed them at opposite ends of the aquarium. or, if your big turtle is a male, he might want to mate. to detract them from chasing each other have a hiding place for the small one and give feeder fish to keep the turtles busy. and i suggest each turtle having their own basking rock. my turtles get along fine.