“In 1753, Linnaeus placed the tomato in the genus Solanum (alongside the potato) as Solanum lycopersicum. In 1768, Philip Miller moved it to its own genus, naming it Lycopersicon esculentum. This name came into wide use, but was technically in breach of the plant naming rules because Linnaeus’s species name lycopersicum still had priority. Although the name Lycopersicum lycopersicum was suggested by Karsten (1888), this is not used because it violates the International Code of Nomenclature barring the use of tautonyms in botanical nomenclature. The corrected name Lycopersicon lycopersicum (Nicolson 1974) was technically valid, since Miller’s genus name and Linnaeus’s species name differ in exact spelling, but since Lycopersicon esculentum has become so well known, it was officially listed as a nomen conservandum in 1983, and would be the correct name for the tomato in classifications which do not place the tomato in the genus Solanum.
Genetic evidence has now shown that Linnaeus was correct to put the tomato in the genus Solanum, making Solanum lycopersicum the correct name. Both names, however, will probably be found in the literature for some time. Two of the major reasons for considering the genera separate are the leaf structure (tomato leaves are markedly different from any other Solanum), and the biochemistry (many of the alkaloids common to other Solanum species are conspicuously absent in the tomato). On the other hand, hybrids of tomato and diploid potato can be created in the lab by somatic fusion, and are partially fertile, providing evidence of the close relationship between these species.”
—Classification section of the Tomato entry on Wikipedia