What is turtle-like about a turtle dove?

European turtle doves spend their summers in Northern Europe and fly all the way to Africa to winter. Not very turtle-like behavior. There aren’t many flying turtles around, and a turtle dove could easily beat a reptilian turtle in a foot race. Looks wise, I see nothing in common with the turtle dove and the common box turtle, or any other turtle you care to mention, for that matter. So where the turtle dove get the name? By the way, as nice as the song sounds, there are no snow-white turtle doves.