Salsa, yes, of course, means sauce. There are many salsas I cook with like mole and roja. These are not chunky, and not for chips.
Pico de gallo is salsa, in fact, that's where we get our version of chunky salsa; tomato, onion, jalapeno, cilantro. The rest of Mexican salsas do not have tomato and are smooth, and those are the ones I prefer. The pepper-based ones you get at the table at real Mex joints.
Now these words take on new meanings in other countries. So the American version of salsa is yes, usually thick and/or chunky. It is based on pico but has more tomato. It is the counterpart to tortilla chips. There are all kinds of variations, like mango, etc. but everyone knows what you mean when you say salsa.
If you want hot sauce in Mexico you may order salsa picante. They will either bring you what you know as salsa or hot sauce unless you are more specific and know the type of the salsa. But hot sauce (salsa picante) in America is the bottled condiment with a (usually) vinegar and/or pepper base made popular by Tabasco and other Louisiana style hot sauces.