Team Logo. The Daytona Tortugas are a team in the Florida State League. They are the High-A affiliate of the Cincinnati Reds. Their name is Spanish for "Turtles." Retrieved from "https://prosportsteams.fandom.com/wiki/Daytona_Tortugas?oldid=13370" Categories: Florida State League teams Teams in Florida Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.