Summary: both are bobs, but have different suspensions and needs.
Suppose the mercury in the clock pendulum completely fills the cavity in that pendulum. As the pendulum swings there is no movement of the mercury relative to the pendulum’s metal case. Therefore, no energy is lost stirring the mercury. And since the clock pendulums are always suspended on a solid shaft of some sort, the pendulum is not free to rotate about its junction with the shaft. It’s mercury does increase its density, though and does help it store more energy so that cutting through the air tends to affect its motion less than a less dense pendulum.
Now, consider the mechanic’s plumb bob on a string. It can have three different motions. It can spin around the axis of the suspending string. It can rotate “side-to-side” around the point from its suspension point where the string joins the bob—-jiggle if you will. And it can swing “like a pendulum” in an arc with a radius defined by the string length. Filling partially (best) or even fully (good) will cause damping of the jiggle and the spin as both of those motions involve stirring of the mercury as the plumb bob shell will tend to move relative to the contained mercury and thus create some heat. The simple swing of the pendulum induced by touching of the pendulum will not be reduced significantly, though a partially filled bob would stir the mercury a tiny bit due to wind resistance. But, the final benefit of the mercury is increased density of the bob and therefore reduced sensitivity to air movement in its environment. I would much prefer the mercury-filled bob as rotation and jiggling are a nuisance when using a bob and air movement can be a problem, though not always.
Denis