If someone is upset, it means they are in an agitated mental or emotional state. If
somebody is angry, it means they are NOT happy, they are hostile. Being angry is
stronger than being upset.
If somebody accidentally spilled coffee all over your new clothes, you would
probably be upset (because it is inconvenient to you), but not angry (because it was
an accident and the other person didn’t do it intentionally).
If somebody purposefully damaged your car because that person hates you, then
you would probably be angry at the person because they did a bad thing on
purpose.
It’s possible to be both angry and upset at the same time. If a teenage boy took his
parents’ car without permission and then got into an accident, the parents would
probably be both upset (worried about their son’s health after the accident) and
angry (because their son disobeyed them and broke the rules by taking the car).
Here’s another example: if you found out you failed a test, you would be upset (but
not angry). However, if you found out that the grading of the test was unfair and the
teacher only gave high grades to his favorite students, then you would be angry
(because an injustice was done).