Sometimes I see a character say この世 and I'm not sure why they don't just say この世界? Is it just an old way of saying it or is there a specific reason?
It is hard to tell the difference but the word あの世 might help you to understand the difference.
あの世 means 'the other world' which you go when you die. So, its opposite この世 means "land of the living" or "this life" or... the world, which is not just the earth. On the other hand, この世界 is almost the same as the earth. Well, you could say that この世界 includes Mars or Mercury or other planets, but for example, 世界一 definitely means 'No.1 on earth'. People say 宇宙一 for 'No.1 in the universe'
Hmmm... it's hard to explain in English..
この世 has a kind of religious or spiritual connotation. Just remember that I'm talking about この世. There are a lot of words which include the character 世, and each word has its own subtle nuances.