Japanese started to eat beef in the second half of 19th century, but they eat more parts of meat than European do. Especially offal, organ meat is popular now and cheap meat to eat for Japanese BBQ.
Popular parts are abomasum, rumen, small intestine and large intestine, which is cut into small pieces and grilled on charcoal. These offal started to be eaten by people in Osaka where many Korean residents live and spreaded to nationwide.
The names of the offal listed on the menu are actually not recognized as proper Japanese words, they are more slangs which can be confused by Japanese too. Therefore you may not get exact translation in English from the restaurant staff!