There's a very specific technique for 'brown-frying' onions in Indian cooking that's distinct from both sauted-until-translucent onions and from caramelized onions, which are cooked (slowly) for much longer. The brown-fried onions (and often garlic and ginger) are used in tarkas that add spices to dal, and to top pilau, and I'm sure in other ways that someone more familiar with Indian cooking could expand on. Julie Sahni discusses the technique and some uses on p. 71 of Classic Indian Cooking, where she distinguishes the technique from caramelized onions and says it "lies somewhere between sauteing and deep frying". She also says that the brown-fried onions (and garlic and ginger) are intrinsic to Moghul cooking, adding color and flavor, as well as helping to thicken dishes, making a delicious gravy.
Sauted-until-translucent onions are often a component of dishes with other ingredients that are then further cooked for some time together -- in a wide variety of cuisines, in almost too many ways to name: soups, casseroles, stir-fries, curries, sauces.
Caramelized onions, being already very thoroughly cooked, are usually added to dishes as a flavoring component -- not combined with too many other strong flavors or subjected to very much further cooking: in mashed potatoes, as a topping for savory puff pastry tarts, in grilled cheese and other kinds of sandwiches, on pasta, in dips, etc.
This might only deepen the argument in your household... <g> Let us know.