I'd translate 世間 as public rather than the world.
For example, 世間の目を避ける。This sentence is translated as "Avoiding the public eye."
世界 means the world. But you can also translate it as "field," like when you wanna say "He is well known in the field of academic study." The translation would be 彼は学問の世界ではよく知られている。
Hope it helps!!