A tautonym is a scientific name in which both the genus and species have the same name. Rattus rattus is an example.
A homonym is a name of a taxon which is identical to the name of another totally different taxon. An example is Echidna - a taxon of spiny anteater and also of Moray eels.
Synonyms are names of a taxon which denote the same organism. Same organisms and different names.