In The World God Only Knows, the manga and anime follow pretty much the same story, but I've read that the light novel, written by Mamizu Arisawa is a completely original story.
What are the major differences between the two story lines? Are there different characters?
This is mostly from memory, so apologies if there are any errors.
The anime and manga both follow the same story line. The novel is in the same setting as the manga; that is to say, Elsie and Keima are still engaging on their usual activities of making girls fall in love with Keima to capture the Runaway Spirits (駆け魂, Kaketama). However, the targets are all new characters, and the stories are original. A few of the new characters were background characters in the anime, but you wouldn't have noticed them if you were not looking out for them.
The novel also assumes that you are familiar with the characters from the original, as some in-universe concepts aren't explained. There really aren't any major changes in the in-universe mechanics, at least none that were memorable enough for me to notice.
It's reasonable to think of the stories in the light novel as additional non-canon additional arcs of the manga. There may be issues as to where exactly the arcs fit in the story, but that's why it's non-canon.
