My understanding of it is:
- Live Feed contains everything, in chronological order,
- while News Feed contains the things that are getting comments. The more comments, the more something bubbles to the top of the News Feed.
Sometimes I will load one or the other and get something strange. Like it will just be status updates and nothing else. It strikes me as another FB bug.
The top thing to understand about FB is that it's extremely buggy. I see things go wrong on that site almost every day.
This, and the way they change things up constantly, are both good reasons not to entrust FB with anything private or important.