Does carrying/dragging a willing/unconscious creature cause half movement as per the grapple rules?

When you carry/drag an unwilling creature that you have grappled, your movement speed is halved.

Is the same true when you carry/drag a willing or unconscious creature (ex: move your friend out of danger) ? Or in other words, a creature that does not resist against your attempt to move it ?

(This assumes that you have a good enough carrying capacity to easily carry/drag an object of the same weight as the creature you wish to move)