Isomorphism  

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1. Similarity of form

1. the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.
2. the similarity in the crystal structures of similar chemical compounds
3. the similarity in the structure or processes of different organizations

 2.  A one-to-one correspondence

1. A bijection f such that both f and its inverse f ⁻¹ are homomorphisms, that is, structure-preserving mappings.
2. a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets
3. A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).