Confusing isn't it.
When drawing a 2D graph youngsters are taught the mnemonic 'Y to the Sky', meaning Y is the axis running from top to bottom of the paper. Works on a vertical computer screen too; the Y axis runs from ceiling to floor. So far so good, but this isn't how dimensions run in 3D on Planet Earth!
On machine tools, as is right and proper, x is right-left, y is forward back, and z is up-down.
String theory suggests we live in an 10, 11 or 12 dimensional world. Just as well only 3 spatial dimensions matter to us – the thought of buying and fitting 11 DRO scales is just too painful!
Dave