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I know Fanuc robots use the XYZ rotation order, ABB uses ZYX and some robots use the ZYZ rotation order. What actually determines this order? is it the way the frames are setup on the DH table? Or is it just the order they chose to solve the IK, and any order could be used? Can anyone help me understand this? TY.

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Any euler angles triplet can be used to represent the orientation of a rigid body (and so of the link a robot). I cannot answer for the particular robots you mentioned, but usually one choose a representation for ease of visualization or to simplify some computation (e.g. if a link rotate around a revolute joint, it simplify the equation of motion to have one the rotation axis aligned with the joint axis).

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