The Indian curry is predominated by the use of a mixture of dried spices. Often the spice mixture or masala is heated in oil or toasted prior to use, to activate the flavors. The combinations are myriad, and if whole spices are used, the shelf life of the basic ingredients can be very long indeed.
The Thai curry also has a complex combination of flavors, but it stems from a much heavier use of a fresh herb base, such as lemongrass, ginger, kefir, and galangal. Equally important, though, is an undercurrent of umami conveyed by the use of fish sauce. I've witnessed the clever use of yeast extract in its place for vegan interpretations of Thai curry.
The Japanese curry is a curious creature. It obviously stems from an Indian heritage, using dried spices, but has a couple of new twists thrown in. First, it is roux based; a convergent cousin to the gumbo and étouffée. Secondly, the Japanese palate is accustomed to a sweeter undertone to the curry, and thus incorporate some kind of sweetening ingredient, such as fruit, into the curry base. Served atop hot rice, it conveys the kind of comfort that wards off a cold day.