Theory is that Tempura is just corruption of word "Tempero"
They reportedly got it from the British Navy, and it has evolved into something distinctively Japanese. The British of course brought it from India.
Japanese curry is sweeter, and has cocoa in it.
My daughter remarked that you can apparently put any random vegetables in Japanese curry and it still tastes awesome.
Because of the warm spices, my first taste of it actually gave me a nostalgic memory of my long gone grandfather who liked to cook "old world" German food. Germany was also influenced by the spice roads and incorporated a lot of these same spices into its cuisine.
https://en.wikipedia.org/wiki/Curry
According to that Wikipedia article, the word originates from Tamil, and:
"Archaeological evidence dating to 2600 BCE from Mohenjo-daro suggests the use of mortar and pestle to pound spices including mustard, fennel, cumin, and tamarind pods with which they flavoured food."