It basically comes from the idea of adding Indian-style spices under various blends sold simply as “curry powder” and adding them to a dish and calling it “curry.” If you look at old American cookbooks, you’ll find various curries that are formed like this; you have stuff like chicken curry salad which is essentially roast or boiled chicken in a mayonnaise-curry powder base; you have curry pumpkin soup, that sort of thing. At Chinese takeaways, at least around here and some I’ve had in England, you will have “chicken curry” on the menu which is essentially just some curry powder mixed into a typical soy sauce-based Chinese takeaway sauce. It’s food flavored with curry powder.
Japanese curry is roux-based. So you make your roux, add curry powder, and build your stew from that. Chinese is kind of similar except thickened with corn starch, and it’s usually not quite as involved as Japanese curry, which can have stuff like honey and apple in it.
I love Japanese curry. It’s one of my favorite comfort foods. Last November I had a prostatectomy and all I could think about post-op was having a bowl of Japanese curry and rice, and that was, indeed, my first proper meal after getting out of the hospital.
Golden Curry is a reasonable introduction to Japanese curry and is extremely easy to make. You just get your vegetables (coarsely cut onions, carrot chunks, and potato) and your protein, add the correct amount of liquid, then add the appropriate amount of curry cubes (directions are on the box.) Some people will add additional ingredients: grated apples, honey, ketchup, kobacha squash, soy sauce, dashi, etc. Everybody seems to come up with their own variations.
My favorite brands are Java and Kokomaru. Oh, and Vermont Curry (which is on the milder, sweeter side, but not overwhelmingly sweet). One of the best expressions of curry is, as mentioned above, with tonkatsu (breaded pork cutlet).
It’s really quite different from any Indian style of curry, but it’s wonderful and comforting in its own right. And it’s really convenient to make, a true throw-a-bunch-of-stuff-in-the-pot weeknight meal. For the effort involved, it has a huge payoff. (And I’ve made it from scratch a couple of times, and really didn’t see the point as the improvement over using cubes [and mixing various brands up] really wasn’t worth it to me for the extra labor involved.)