Someone who's blue feels sadness, like a little girl whose best friend has moved away.
Use the noun sadness when you're talking about sorrow. Sadness may be the overwhelming mood at a funeral, for example, or an elderly man might describe his life's greatest sadness as letting his childhood sweetheart get away. An interesting thing about sadness is that its original meaning was "seriousness." It wasn't until the 1600s that it came to mean "full of sorrow."