First, I should clarify that all of the antediluvian kings are likely entirely mythological; we have no independent attestation of any king before Enmebargesi(attested in the Tummal Inscription and a engraved bowl) and they all have implausibly long reigns. With that in mind, they seem to have been entirely separate people; the "Instructions of Shuruppak" speak of Zisudra as Ubara-Tutu's grandson and he is regarded in virtually the entire Sumerian literary tradition concerning the flood as the sole survivor and hero. Also of note here are various other king lists(most notably the Dynastic Chronicle and a version of the Sumerian King List differing from the prism in the Ashmolean museum) list both Ubara-Tutu and Zisudra as rulers of Shuruppak; if anything the omission of Zisudra from the the standard text of the "Sumerian King List" is rather unusual compared to other king lists. One interesting suggestion I've turned up about the list by Y.S. Chen in The Primeval Flood Catastrophe: Origins and Early Development in Mesopotamian Traditions is that Zisudra was omitted because his position as the flood hero and his eternal life proved incompatible with the purpose of the King List as a document legitimating the hegemony of the city of Isin by putting it in the succession of kingship from the earliest times in human history. Hopefully that helps; feel free to ask any followup questions you have.