I know that enantiomers are mirror images which are not superimposable on each other.
What about mirror images which are superimposable? Are they necessarily the same molecule? Is there a particular term for them?
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If two molecules are superimposable, they would by definition be the exact same molecule. There is no chemical test you could perform to differentiate them. This is true for all achiral compounds.
The most interesting case of this would be a class of molecules called meso compounds. They contain multiple stereogenic centers, but due to an internal plane of symmetry (or certain other symmetry elements), reflection of these molecules across a mirror plane results in superposable mirror images.