Basically, I think chutney and salsa just come from different languages. It's not just a matter of being cooked, because I have had cooked salsas before. Salsa has been taken over as a much more widely used word, though.
Usually, if I *just* hear the word salsa, I'll assume that it's a Mexican derived dip that contains some combination of tomatoes and/or tomatillos, onions, hot peppers, lime juice and salt as the main ingredients, the same way if you just say "pesto" I'll assume an Italian paste of basil, pine nuts, garlic, olive oil and parmesan cheese. If you add qualifiers, though, the varieties can expand widely.