Correspondence vs Mapping in ontology

Question

I'm currently studying about ontologies and ontology alignment and I'm a bit confused about the concepts of correspondence and mapping. I have looked into many bibliography and yet none manages to point out their differences. From what I understand, correspondences seem to refer to the specific relationships of entities in ontologies, while mappings refer to those correspondences. Could someone clarify the key differences between correspondences and mappings? Is there any way you can provide me some simple mathematical examples to make it more understandable?

Thank you in advance!