Why is the English word "curry" used for all these different dishes?
"Curry" is based on the Tamil word "Kari", which refers to any of various highly-spiced side dishes intended to be eaten over rice. Englishmen from the British East India Company encountered the Tamil word in their first explorations of the subcontinent, applied it more broadly to pretty much all Indian dishes, and used it in preference to words in other Indian languages.

By the early 19th century, "Curry houses" were established as restaurants in London.  As a result, when British travellers encountered highly spiced stews in Siam and Japan, they called these "curry" as well.  Many of these dishes were descended from Indian cuisine in any case.

If you're interested in this, I highly recommend getting a copy of Curry: A Tale of Cooks and Conquerors.  It'll give you a history of the last 600 years of "curry", and recipes besides.