What are identical molecules?
Identical compounds have the same chemical and physical properties (and other properties too). 

Of the two types of stereoisomers, diastereomers (non-mirror image stereoisomers) are clearly nonidentical. Consider the isomers of tartaric acid. Meso-tartaric acid and (+)-tartaric acid have different melting points (165 $^\circ$C and 171 $^\circ$C, respectively). They also have different acidities.

The (+) and (-) isomers (enantiomers) are more challenging, but they are distinguishable by one physical property - the way they rotate plane-polarized light. If the two molecules were identical, they would not be isomers - we would not be able to distinguish them. If they are distinguishable, they are not identical.