shout: can be just speaking loud, and also for a short time scream: it's definitely louder, and often you are not speaking, just saying "aaaaaargh"! yell is close to shout, often in anger

They can be used interchangeably in most sentences. But if you want to be very specific: a shout can be words, especially words yelled in anger, like in the phrase "shouting match" which refers to a loud, angry fight that never becomes physical fighting. It could also be used to refer to a hoarse, loud cry, but this is a less common usage. It is more common for the term to be used for male voices than female. A scream could be words, but is much more likely to be just a very loud, high-pitched noise. Most people would think of screaming as being louder than shouting. It's more common to apply scream/screaming to female voices than male.