When you become angry with someone, you sometimes end up `shouting at' them. You say whatever it is you want to say in a loud and angry voice. In this case, you are being aggressive.
The coach shouted at the players when they turned up late for practice.
When you `shout to' someone, you are calling out to the person. The person is probably far away and therefore you use a loud voice to get his attention.
He shouted to us to come and join him on the boat.