The judge refers to someone who will be in charge of deciding certain aspects regarding a case. For example, there is someone who is being charged with a crime in court. The judge, together with the jury, will help decide if the person is guilty or not. A judge would typically need to have years of education and tests before they can reach this position.
Justice is someone who can officiate weddings and other ceremonies but will not have any power to judge people for their actions because he has not undergone any legal training for that. He can witness legal documents, but he does not have any power to make one document more important than the other.