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Sudoku round 2, Figures Sudoku

The instructions for sudoku 7 in round 2 (Figures Sudoku) say that "Dotted areas with the same shape must contain the same set of digits".
Are mirrored and/or rotated shapes considered as same?

They are, yes.
A more mathematically accurate formulation of the instructions could be "Congruent dotted areas must contain the same set of digits".

Sometimes same shape can mean just a translation, sometimes it can include rotations as well, and sometimes it can also include reflections. To really stretch things it could plausibly included scaling the size. Rather than find the most mathematically precise way of describing these concepts, which some solvers may or may not know, i think it is better to simply state whether you intend to allow reflections or rotations. The instructions are a form of communication, so that if someone fails to understand the rules then your instructions can usually be improved.