After the war, the Japanese government changed its attitude (presumably under the guidance of US occupation forces), and declared that both the instructed system and the Hepburnian system may be used officially (both of the systems were modified a little bit in this step). The Hepburnian system is called the standard system hereafter. Most Japanese scientists use the standard system.
This is one of the causes of confusions in the method of writing Japanese in Roman characters.
The differences between the instructed system and the standard system are: