plotting - Plot3D: ColorFunction depending on (x,y) or z

While trying to answer this question I found out "weird" behavior of ColorFunction

Plot3D[x y, {x, -10, 10}, {y, -10, 10}, PlotRange -> Full, 
 ColorFunction -> Function[{x, y, z}, Hue@(x y)]]

gives incorrect colors

the virtually identical code (from naive point of view)

Plot3D[x y, {x, -10, 10}, {y, -10, 10}, PlotRange -> Full, 
 ColorFunction -> Function[{x, y, z}, Hue@z]]

gives correct plot

Also if you disable ColorFunctionScaling as many posts (e.g. this) suggest

Plot3D[x y, {x, -10, 10}, {y, -10, 10}, PlotRange -> Full, 
 ColorFunction -> Function[{x, y, z}, Hue@(x y)], 
 ColorFunctionScaling -> False]

the colors are really messed up

So the question - why are the first two plots different? A bug?

I'm using Mathematica 11.1 on Linux.

Answer

As the documentation on ColorFunctionScaling says,

ColorFunctionScaling is an option for graphics functions that specifies whether arguments supplied to a color function should be scaled to lie between 0 and 1.

In the first plot, $x$ and $y$ are both scaled to the range $[0,1]$. This means that the ColorFunction does not receive $x$ and $y$, but rather $(x+10)/20$ and $(y+10)/20$, and the color is then the hue of $(x+10)(y+10)/400$.

In the second plot, $z$ is scaled to the range $[0,1]$. This means that the ColorFunction does not receive $z$, but rather $(z+100)/200$ as the third argument.

In the third plot, the number of PlotPoints is too small and thus you see Moiré effects.