Sauce comes from the Latin salsa, which means salted food, deriving ultimately from the root sal, for salt.
The Spanish word salsa, nabbed directly from the Latin, simply means sauce in a generic way. But the Spanish salsa has entered English as a word separate from sauce, referring to the chunky condiment we dip nachos in.
Salsa as a style of dance apparently picked up its name in the 1970s. The connection seems to be that it’s a mix of many pieces of different styles, and/or that it’s spicy and hot — either way, it derives from the earlier, food-related meaning.
You don’t often hear people described as saucy anymore — at least, not in American English — but you see it in older books sometimes. Someone who’s saucy is impudent, bold, irreverent. The person, like a sauce, has a strong and striking “flavor.” This branch off the sauce tree emerged around 1520; before that, saucy just meant, well, related to sauce.
Saucy sounds a lot like sassy, and sassy means … let’s see … impudent, bold, irreverent. About the same meaning, about the same sound. Could it be … ? Yep. Sure enough, sassy is nothing more than an American variant of saucy, formed sometime around the 1830s.
So whether you’re dancing the salsa, or giving somebody sass, it’s really all about the sauce.
After all, sauce is also internet slang for source. Appropriate, no?
Most of this information comes from the always helpful and endlessly fascinating Etymonline.com.