From Bioinformatics.Org Wiki
The Medical Informatics FAQ provides the following definition:
"Biomedical Informatics is an emerging discipline that has been defined as the study, invention, and implementation of structures and algorithms to improve communication, understanding and management of medical information."
That FAQ also points here
Aamir Zakaria, the author of the FAQ, emphasises that medical informatics is more concerned with structures and algorithms for the manipulation of medical data, rather than with the data itself.
This suggests that one difference between bioinformatics and medical informatics as disciplines lies with their approaches to the data; there are bioinformaticians interested in the theory behind the manipulation of that data and there are bioinformatics scientists concerned with the data itself and its biological implications. (I believe that a good bioinformatics researcher should be interested in both of these aspects of the field.)
Medical informatics, for practical reasons, is more likely to deal with data obtained at "grosser" biological levels---that is information from super-cellular systems, right up to the population level---while most bioinformatics is concerned with information about cellular and biomolecular structures and systems.