Broths & Stock are technically different. A broth is the finished product whereas a stock - made by simmering various ingredients in water - is the base to make a broth. A stock can become a broth.
Chilis are generally combinations of beans, tomatoes and their sauces and some type of meat (this of course is optional). Chilis can range from nuclear hot to a gentle pepper flavor, and everything in between.
Chowders are thicker soups, usually enriched with flour or crackers to give it that extra bite. Seafood is a common ingredient in chowders such as clam chowder.
Stews are typically hearty soups with a thicker, meatier and chunkier consistency since the ingredients are not as finely chopped. The bases used to make stews may not be as watered down either.