Matrix rows or columns are traditionally listed under $(x,y,z)$ order.
Cyclically change the pairs under consideration i.e $(x,y)\to(y,z)\to(z,x)$. The pairs $(x,y)$ and $(y,z)$ show up in the same order in the matrix but the $(z,x)$ shows up in reverse in the matrix. That is the cause of apparent discrepancy but really there is no discrepancy.
For example write
$x'=x\cos \alpha - y \sin \alpha$
$y'=x\sin \alpha + y \cos \alpha$
now change $(x,y)\to(y,z)\to(z,x)$ and $\alpha\to \beta \to \gamma$ and write the three matrices to see how $(z,x)$ part gets flipped.
Edit:
If you want them to look alike then give up the matrix notation and instead write
$y'=y\cos \beta - z \sin \beta$
$z'=y\sin \beta + z \cos \beta$
And
$z'=z\cos \gamma - x \sin \gamma$
$x'=z\sin \gamma + x \cos \gamma$
In each instance if you try to write $\left[ \matrix{ x' \cr y' \cr z'}\right]$ in terms of $\left[ \matrix{ x \cr y \cr z}\right]$ you will see that the mystery goes away.
If you know the sequence of roll, pitch and yaw that you want to do in succession, you can find their matrices and multiply them together in the right order, and the three operations are performed "simultaneously."
The order is important because the group of rotations is nonabelian. If you can produce a matrix for each of these operations, then you can produce a single matrix combining all of them.
Best Answer
First, you cannot add or subtract Euler angles. They are not vectors. You need to convert the Euler angles to a representation that can be composed such as a rotation matrix or unit quaternion. If $R_b$ is the base line rotation matrix and $R_i$ is a given rotation matrix, then you can measure rotation w.r.t. the baseline using the following formula $R = R_b^{T}R_i$.
To convert from Roll, Pitch, Yaw angles, you need to compose three rotation matrices about the Z, Y and X axes (assuming that Z ~ yaw, Y ~ pitch, and X ~ roll in the local frame). This is just a composition of the three coordinate rotation matrices:
$$R = R_z R_y R_x.$$
To get the euler angles back I refer you to the following: https://stackoverflow.com/questions/11514063/extract-yaw-pitch-and-roll-from-a-rotationmatrix