symmetry operation- a transformation between indistinguishable states.
transformation- a move such as a rotation, a reflection, an inversion, or even not moving at all.
A symmetry operation moves an object, such as a molecule, in a way that after the movement is complete, the object looks the same as it did before the movement.
If you know what a water molecule looks like, try to imagine how you can rotate it 180 degrees and the two hydrogen’s will exchange places. You know that the hydrogens moved, but an instrument that takes a measurement for spectroscopy will give the same result for both before and after because it doesn’t know.
The words “Symmetry Operation” make you think about the action. You should also think about how the things in Geometry cause these operations to results in that indistinguishability, and the word for that is Symmetry Element.
Rob Sterling 