Having tasted a 'Kobe' flat iron steak quoted as 'Wagyu' and not knowing what 'Wagyu' stood for, I did a little research.
To keep it simple Wagyu refers to all Japanese beef cattle ('Wa' meaning japanese and 'gyu' stands for cattle). This type of breed produces 'Kobe' beef. It is so labeled because 'Wagyu' were first bred in the city of Kobe some 170 years ago.
They were originally a cross breed of Asian cattle with European breeds that took place in the late 1800's.
Although it was closed to cross breeding in 1910, there are various regional lines in Japan.
For more details on that read Cattle Today's page.
They are now bred in US ranches such as Morgan Ranch in Nebraska and others in California.
The high price of 'Kobe' beef is due to its small production as lean beef is more widely distributed and popular since the 1940's.
'Wagyu' are known for their marbling and fat content which makes for a very tender meat.