Japanese Curry?

Ok, I have had Indian Curry, and it wasnt bad, but not a big fan of over spicy hot stuff. And see that Japanese Curry is more sweet. I keep hearing Curry mentioned in my animes, and I have an idea what it is. But looking at maybe trying to find a restaurant nearby here in Pittsburgh, that serves it. So I can taste how it should, and maybe start trying to eat it myself, since rice is already something I eat a lot of, when cooking. I am pretty sure, I am looking for the wrong thing when looking at restaurant menus online. I see maybe I should be looking for Katzu, instead of Curry. But figured would ask here, since folks here would no better. :) So when looking at menus, what names should I be looking for, that are actually what I am looking for. Thanks in advance

The district in which I live is famous for curry. I remember that there are many curry shops and one of them opened a shop to NY. It is a style which sets a cutlet and the minced cabbage on curry.