What is the difference between DR. and Dr.?

DR.

This is used for people who have attained heights of academic excellence and have done research in some particular aspect of the concerned subject. They have been awarded the degree of doctorate.

Dr.

This is used for people who have attained efficiency in some branch of the medical sciences and are busy in the amelioration of sickness and disease from humanity at large by serving the people (as the savants) or by making research into the why and wherefore of a disease and developing suitable remedies by way of medicines.