I drew the graphs of $f(x,y)=xy$ and $g(y,z)=yz$ on Geogebra $3 \text{D}$ and I found both of them similar. How is this the case? How are the two graphs $(x,y,xy)$ and $(yz,y,z)$ similar?
For example: $f(2,3) = 6$ gives the point $(2,3,6)$ but $g(3,6) \neq 2$.
So how exactly is the function plotted? I don’t think it’s in the way I assumed.
Geogebra doesn't know that your $y$ and $z$ carry special meanings.
It just interpreted $y$ as the first input and map it to $x$ and $z$ as the second input and map it to $y$.
You might like to plot $z=xy$ and $x=yz$ explicitly.