Really interesting question.
Yes. There are standardized "RGB" color wheels.
An RGB... which is in reality an RYGCBM color wheel is pretty much a mechanical representation.
There are some variations, such as an HSB, HSL, or HSV wheel but the "main" component of the round part (wheel) is the Hue, with some "normalized" angles. Look at this google image search https://www.google.com/search?q=hsl+color+wheel
They are different transformations and projections of an RGB cube (Which renders a hexagon)
They are "standardized" in the applications that want to adopt them (but no one is forcing them to do so). For example, they are adopted in Corel applications, Gimp, Inkscape, a ton of painting programs that I know, MediBang, MyPaint, Dogwaffle, 3D programs, Blender, Sketchup, video editing programs... Any program that I checked that I have installed on my computers has one form or another of this Color wheel... except Photoshop! (I currently do not have some other adobe programs installed)
Because there is a ton of variations on the color solids.
A color model is not a 2D shape, it is a 3D volume because we can separate it into 3 Dimensions. And there are quite a number of 3D volumes trying to describe color.
You can choose different planes to intersect to form a 2D representation. But you also have some other color models that even on the main plane have different opposites, like the Lab Color model.
As I said. The standard color wheel is a mechanical representation, a cut from a 3D mechanical volume. But there are other volumes, for example, the Munsell model.
You can see that the model is not a regular shape, because humans are more susceptible to recognize variations in some hues than others.
In this other example in the zone C, we detect fewer variations than the zone D.
The adobe wheel is not an RYB one.
I assume that those color wheels have artistic freedom and interpretation of harmonies because they are intended to provide a perceptual-based tool, so that is (in my opinion) each one has adopted a specific model-variation-interpretation.
And I am not sure
Of other color models, for example, the Lab* model has some variations, implemented to some extent in Photographic applications, like white balance in cameras. But to tell the truth I have not a good amount of information about it.
Are thoose circles RYB?
Based on @Kadilov request, I add this part about the color wheel used in the linked sites on the question.
paletton.com seems to have in fact an RYB color wheel. You can see how the colors correspond to the vertices in a hexagon.
But in the case of Adobe one... I have no idea. It is not RYB, neither an RGB+CMY nor Lab. I have the feeling it is trying to simulate some printing colors on the screen.