Spurs drive, revolving live centres they come in different sizes and styles there are multi centres, all comes down to what you want, and what you want to pay. you by cheap live centres and thats what you get, you pay more you get better bearings and a higher standard of item. take a look at woodcraft and places, its not rocket science.
Most cheaper ended lathes come with there drives and spurs but of a cheap nasty nature the spurs are genrally a blunt end and needs to be reground. If you use a chuck then look at spurs that fit the chuck saves a lot of bother taking chucks of when you do some spindle work, just drop the spur into the chuck and your away.