Wikipedia has the matrix below when rotating in the following order Z -> Y -> X.
This article shows the same rotation but ends up with a slightly different matrix where some elements are multiplied by -1.
If I multiply the matrices by hand I get the second result. Why is there a difference between the two ?
To begin with, in the green matrix the value (3,2) should be $$ sin\psi \, sin\theta \, cos\phi - cos\psi \, sin\phi $$
Then, in the article the rotations are not right-handed like in wiki. For example, if you rotate the point (1,0,0) for $\frac{\pi}{2}$ around z-axis right-handed, you expect to get to (0,1,0). But instead, using $R_z$ from article's equation 4, you get $$ \begin{pmatrix} cos(\frac{\pi}{2}) & sin(\frac{\pi}{2}) & 0 \\ -sin(\frac{\pi}{2}) & cos(\frac{\pi}{2}) & 0 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = $$ $$ \begin{pmatrix} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ -1 \\ 0 \end{pmatrix} $$
You can check the other two rotation matrices as well and you will see that they are also rotating left-handed.
The way to get from left-handed to right-handed rotation is by changing the "direction" of your rotations, i.e. swapping $$\psi \rightarrow -\psi$$ $$\theta \rightarrow -\theta$$ $$\phi \rightarrow -\phi$$
Doing so, and using the trigonometric identities $$ cos(-x) = cosx $$ $$ sin(-x) = -sinx $$ wiki and article matrices will be the same.