Enantiomerism and Diasteriomerism
Your definition of enantiomer is correct.  

This simple further classification might be helpful.  Let's take 2 molecules with the same molecular formula.  These molecules are either constitutional (or structural) isomers or stereoisomers.  If they have different structures (or connectivity patterns)  and are separated by an energy barrier, then they are constitutional isomers.  If they have the same structure or connectivity pattern, then they are stereoisomers.  

Among stereoisomers there are 3 classes that we can place a pair of molecules into.  Take any two stereoisomers and compare them, they are either


the same (2 identical molecules)
mirror images of one another (enantiomers)


If they are not the same or enantiomers, then they are


different, and we call them diastereomers.