Yes, but between Arizona and Florida I'm sure there are regional differences in which slang names are used for each sort of ant. So in my region of FL, "piss ants" are also referred to as "sugar ants"; in our case, they're tiny, black, don't bite, just annoy you - and occasionally take over your kitchen...while "carpenter ants" are indeed huge, but from what I recall someone telling me years ago, aren't true carpenter ants, because they don't have wings or fly, and "red ants", also know as "fire ants", are tiny, red, angry little things that often attack in swarms and can sense the vibration of your footsteps, even on grass, from up to 25 feet away. Red ants are by far the most fascinating and industrious ants FL has, but they are not even native to the US.

I've been swarm-attacked so many times by our red ants, my ankles are permanently scarred from them (I used to garden a lot more than I do now, and I even worked as a landscaper for a few years, which definitively added to my overall red ant agony).