"Curry" is used by Indians to describe freshly-made solid-ish vegetable/meat dishes that are always eaten with rice or flat breads like roti and parathas. They aren't eaten by themselves. They are also meant to be eaten hot. It's important that the "main event" is the carbs, with the curry accompanying them. This is both a broad and narrow definition. It's broad because you can make a curry out of any vegetable and any meat, with practically any spices. It's narrow because it has to solid-ish and be eaten with rice or flat breads. A soup like sambar or rasam mixed with rice isn't considered a curry, but it's not a soup per most people's standards either. A soup isn't a curry because it's not primarily eaten with rice or flat breads. A pickle isn't a curry because it might take months to be prepared; it's not meant to be eaten fresh. A mango chutney is not a curry because it's not meant to be eaten hot. (Note that the Indian definitions of "pickle" and "chutney" vary from the American/British usages. In India, a "pickle" is a preserved fruit/vegetable/meat in oil, chili powder, and other spices. A "chutney" is a freshly-made dish of diced fruits/veggies, often reduced to a paste with a blender.)
This is a sort of definition that's intuitive to Indians.
The problem Indians have with foreign usages of "curry" are, I think, with them not respecting this definition, and using the word to refer to pretty much all Indian food. "Going to get some curry" sounds like you don't care about even the basic differences in the cuisine you're eating. That all said, I understand that I'm undermining my own argument. It's rather subtle to tell a curry apart from another Indian dish.
Indian people eat plenty of things aside from rice/roti + curries. You have kebabs, biryanis (rice baked with meats), sandwiches (from Vada Pav street food to everything else), noodles (Indo-Chinese cuisine), a million buttery, saccharine sweets, unique breakfast foods like dosas and idlis, and so so much more. How can you have a country the size of India with at least 20 major cuisines and languages, in a country with influences from East Africa, Central Asia, Tibet, South East Asia, and Western Europe, without tremendous culinary diversity?