Use the adjective wrong to talk about something that is factually incorrect. You thought your paper was due a week from Friday, but you were wrong. It's due tomorrow. Better start typing!
You can use the word wrong to describe something that deviates from your moral principles. You might believe that the death penalty is just wrong, but not everyone agrees with you. The adjective wrong can also describe something that is inappropriate for a certain purpose. It's frustrating to get all the way home from the store before you realize you grabbed the wrong kind of milk — buttermilk instead of two percent.