As Brian said, "upset" can refer to several different negative emotions. If you see a small child crying, you might ask the child why he/she is upset. It doesn't always mean "angry." Literally, to "upset" something is to topple it or turn it over (usually with a negative result). For example, if you "upset" a glass of water, you knock it over, and it spills. So if your emotions are "upset," they have been turned over, or turned to the wrong direction. That could mean that you're angry, or it could mean that you're having some other negative emotion.

Angry is more hostile. Think of fighting. Losing control of yourself. Screaming! ANGRY!!! Upset can mean frustrated, sad, disappointed separately, or all at the same time. Upset is a more generalized feeling. Angry is more specific to feelings of hostility and negativity. I was upset that my boyfriend didn't call me. When I heard he was with another woman, I became angry!

As adjectives, upset is an emotion felt within oneself, meaning feeling distressed, angry or unhappy, whereas angry is displaying or feeling anger.

Upset is more like "sad" and angry is like "furious".