"shout", "scream", "yell" are all similar.
Scream + yell are often used when people are angry.
Shout can be used when you are angry but also when you need to talk loud. For example:
It was so loud in that restaurant that we had to shout to hear one another.
"cry" is what you do when you are sad and tears come out of your eyes. "I cried at the end of the movie when the dog died."
"cry out" is what you do when, for example, you are hurt or surprised.
"cry out for help" is a set expression.