There is no distinction between the terms "Dr." and "DR." A person with a PhD or a medical degree can put Dr. or Dr. in front of their name. They are both acceptable. The only people who use the full form of their degrees are those who have had them certified by a professional organization. These people use Dr. or Dr. before their name to indicate that they have been awarded a degree from an institution recognized by society. Most people use just their last name after their degree. So, yes, you can write DR or DR without any problems. It's not common but it's possible.