The main question asked by people looking at Capstan and Turret lathes, is "What is the difference?".
This most easily explained by the following two pictures.
The first picture shows a Capstan lathe turret, and this description is the cause of the confusion. The turret is the toolholding and rotating part which is carried on a fixed but movable saddle. The turret itself moves on the saddle.
The second picture shows a turret off a Turret lathe, and the turret itself moves with the saddle at all times. This moving saddle on the turret lathe is what makes it different in operation from the Capstan machine.