They can be used in similar ways. 'sad' is like what you probably think of when you think of sad: someone crying for some reason. 'upset' almost implies that something happened to the person who is upset. And 'upset' doesn't always mean 'sad'. It could mean someone is angry or annoyed as well. 'sad' does not imply angry or annoyed, just sad, grief, hurt.

Sad is when you feel an emotion that makes you want to cry, for example. Upset is when you feel an emotion that may make you a mixture of sad, frustrated, angry, annoyed and wronged. He feels sad. She is sad. They are upset.

Examples: Simon is sad because his dog died. The child could not go to the ice cream store so she was sad. Amy became sad after hearing about the accident. (implies that she cried, she felt really down) Amy became upset after hearing about the accident. (implies that she may have been angry, scared, anxious, and sad) Brad was upset yesterday because he had an argument with his girlfriend. When you push me, that makes me upset. Actually, you could replace any of the 'sad' or 'upset' in those sentences with the other word and they would have similar meanings.

He felt sad, quite upset.