I am aware of two common types of color wheels - RYB and RGB, but it seems that even two wheels of the same type can look different in different software. Let's take two popular online services, Paletton (http://paletton.com) and Adobe Color CC (https://color.adobe.com), both using RYB type of color wheel.
First, make an "Adjacent" scheme in Palleton with base color being green (#00FF00) and leaving "Distance" with its default value. In this situation, two other colors that Palleton suggests are #00FFFF and #AAFF00. Looking at the wheel we can be sure that the angle between the base color and these two looks equal.
Now select a "Custom" scheme in Adobe Color CC and type in three mentioned RGB values. On Adobe website the angle between #00FFFF and #00FF00 will look greater than the angle between #00FF00 and #AAFF00.
Does this mean that there is no such a thing as a standardized RYB (or RGB) color wheel? Previously I thought that with a beginning of the Computer Age it became possible to digitally render such things using some well-known algorithm, so all color wheels in graphics software should look really close (at least without such clearly visible differences as I describe in this question).
Answer
Really interesting question.
Yes. There are standarized "RGB" color wheels.
An RGB... which is in reality a RYGCBM color wheel is pretty much a mechanical representation.
There are some variations, such as a HSB, HSL, or HSV wheel but the "main" component to 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 an hexagon)
They are "standarized" in the aplications that want to adopt them (but no one is forcing to do so). For example they are adopted in Corel aplications, 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)
No
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.
Perceptual models
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 suceptible to recognize variations in some hues than others.
In this other example in the zone C, we detect less variations than the zone D.
Artistic liberty
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 in 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 an hexagon.
But on the case of the adobe... I have no idea. It is not RYB, neither an RGB+CMY or Lab.
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