Confused about Tone Curve: Parametric vs Point Curve

I don't know the exact answer, but the history might provide some insight. 

Lightroom Classic 1.0 was released in 2007, and its Point Curve is probably based on the Curves in Photoshop that existed for many years before that. So the Point Curve is the starting point. It has the longest history by far, is widely taught, and is a standard tool now found in many other Photoshop-like apps.

The Parametric Curve was introduced later, in Lightroom and Camera Raw but not in Photoshop. I think the Parametric Curve was marketed as an easier way to use a curve, because instead of having to learn how to manually decide where to place the points and how to move them, you can just move some labeled sliders.

But they basically do the same thing. When you edit the curve, each tonal level starts at one value, and your edit shifts them to another value set by the curve. That's why on the Point Curve, each point has an Input and Output value.

What about the Refine Saturation slider? I don’t know why it’s only in the Point Curve, but this is my guess: The Point Curve has always been the “pro” option, because it’s more difficult to understand and learn than the Parametric Curve or (in Photoshop) the Levels command. They might have decided that Refine Saturation should be in the curves type that’s more widely used by pros, and for now, they decided not to add it to the Parametric Curve because it’s more of the “easy” option. But again, that’s just my guess. Maybe they’re open to adding Refine Saturation to Parametric Curve later, but that isn’t something we users would know.

As JohanElzenga pointed out, another difference is that the Point Curve lets you separately edit each RGB channel. That is two advanced features that Point Curve has that Parametric Curve does not, contributing to the notion that Adobe might think Point Curve is the “pro” version and Parametric is the “easy” version.

#1 - More or less correct. A big difference is that the point curve has individual channels as well, so it is also a powerful color correction tool. The point curve used to be on its own, but because many people found it too challenging, Adobe added a simpler version.

#2 - No idea. Perhaps because the parametric curve is aimed at people who may not understand what the Refine Saturation slider does...