Pyramids, Step Pyramids, and Ziggurats. What's the difference?

I always thought of them as:
classic Egyptian pyramid, 4 smooth sides, rising to a point at the top.
ziggurat as a stack of boxes, each one smaller than the one below it. Like a pyramid built out of legos.
A step pyramid as being sort of in between.

So what are Mayan temples, like those in Chichen Itza?

I always see them called pyramids, but they don’t have smooth sides, and they don’t come to a point at the top. Instead they have a platform on top, with a temple/structure occupying it.

In addition, most of the definitions i find online for ziggurat (type that enough times and that word begins to look really really weird) specifically call it a Mesopotamian structure.

Are there hard lines separating and defining the 3 structures?

I think part of the problem is that the word “pyramid” has stricter and looser definitions, and unless a speaker or writer is careful to tell you what they mean by it, you can be sure you don’t know.

As far as ancient buildings are concerned, I think that ‘pyramid’ covers just about any regular shaped construction with triangular sides and a top smaller than its base.

Mathematically, of course, a pyramid is defined as "a structure whose outer surfaces are triangular and converge to a single point at the top"

Little engineering expertise was required to build an impressive structure (and more-or-less permanent) this way - the main problem being the logistics of getting the heavy stone to where it was needed.

Ziggurat seems pretty well-defined, since it’s the actual Akkadian word for a building with a certain architecture and cultural/religious significance. Perhaps we should adopt the Egyptian and Mayan words, respectively, for the other two main types?

While there’s plenty of conceptual overlap, I’m not sure there’s much confusion in practice.

Let’s start with Ignotus’s point. “Ziggurat” is unambiguously Middle Eastern. No real possibility for confusion there.

For Egypt, there’s a pretty clear divide between step pyramids and “true” pyramids. But they are all pyramids.

The arguably awkward case are the Mesoamerican cases. Since they are rather obviously analogous to ziggurats. But they are invariably described as pyramids.

Given this stable (if possibly somewhat arbitrary) classification, it’s probably not terribly helpful to retrospectively complain about it.

The term Ziggurat is frequently used for any stepped building. Not all of them are pyramids. The John C. Hodges library, for example, is often called a ziggurat, but isn’t a pyramid by any stretch. An Incan temple might be both a ziggurat AND a pyramid.

It seems to me that this is a misuse of terminology. I don’t think you should equate a tent with a tipi or a kåta. Sure, they’re more or less equivalent with respect to their bare function; but they have certain cultural connotations that are really important. There are rules for how to enter and sit down in a kåta as a guest that don’t correspond to anything with respect to a tent or a tipi. And certainly the other way around.

By the time Europeans saw the Mayan pyramids, the ones in Egypt had lost most of their sloped stone covering and looked equally stepped. (The middle one at Giza still has some of the very top smooth stones…)

The true “Step Pyramid” is the original one by Imhotep at Saqqara - the very first Egyptian pyramid.
IIRC didn’t the mound builders in central USA also build “pyramids” of earth?