This is an absolutely rudimentary question but I want to get clear from the off with my study of Group Theory.
If we have a rectangular object that can physically be picked up, but which we are using to represent a 2d rectangle, comparing picking it up and "flipping" it by 180° about its vertical or horizontal axis with applying "mirror symmetry" about those axes:
Are these actions functionally equivalent?
Is there ever a need to distinguish between them?