What's the difference between tilde(~) and caret(^) in package.json?

After I upgraded to the latest stable node and npm, I tried npm install moment --save. It saves the entry in the package.json with the caret ^ prefix. Previously, it was a tilde ~ prefix.

1. Why are these changes made in npm?
2. What is the difference between tilde ~ and caret ^?
3. What are the advantages over others?