operational amplifier - comparator schematic symbol

This schematic appears in a recent question. The triangle may be an op-amp or a comparator, because they both have the same connections. (Why) isn't there a separate symbol for a comparator? The functions of op-amp and comparator are very different.

Or from the document @boardbite writes about in a comment:

Answer

I've never seen a different symbol for comparators, so I had to make up this one:

The hysteresis symbol refers to the hysteresis which is often built-in into the IC, or otherwise is almost always needed in the circuit. Does this make sense?

edit
Olin objects. He's right: it suggests a built-in hysteresis, rather than a required one. So second attempt: