Anger can be the result of hurt pride, of unreasonable expectations, or of repeated hostile fantasies. Any situation that frustrates us, especially when we think someone else is to blame for our loss, is a potential trigger for anger and aggression. It is the feeling we get when we don't get what we want, when something interferes with our gaining a desired and expected goal. Anger is feeling mad in response to frustration or injury. You don't like what has happened and usually you'd like to get revenge.
Aggression is action, i.e. attacking someone or a group.
It is intended to harm someone. Such thoughts and dreams suggest anger, of course, but are not aggression as I have defined it here. When our aggression becomes so extreme that we lose self-control, it is said that we are in a rage . Anger can also be distinguished from hostility which is a chronic state of anger. We know when we are very mad, but anger and aggression come in many forms, some quite subtle.