I suppose it started with the O.G. Ramen Burger, then there was Samurai Burrito, and Toro Burger. For a lack of a better word, I'll call it fast-food-fusion, where Japanese flavors and ingredients are incorporated into the Western ideas of sandwiches, burgers, and burritos.
Herewith are two more entrants into this genre. The first is Mr. Katsu, which opened recently in Fullerton at 3165 Yorba Linda Boulevard, serving katsu sandwiches–deep fried pork cutlets stuffed between two toasted slices of bread (which is, by the way, something Cream Pan in Tustin has always offered). Also on the menu: yakisoba sandwiches (yes, Japanese stir-fried noodles akin to chow mein) but also good ol' grilled cheese.
Musubiya Balls & Burgers, on the other hand, specializes in musubis, those triangles of rice wrapped in crispy nori and filled with meat and sometimes SPAM. Those are the "balls" part of the "Balls & Burgers". The "burgers" are the "ramen burgers", using two discs of pan-fried ramen as bun. Musubiya is at 3701 S Harbor Boulevard, Santa Ana.