If you put a block on the table, it will rest, and if you put a ball, it will start rolling.

If you put a block on the table, it will rest, and if you put a ball, it will start rolling. Does it follow from this that a bar lying on a table is acting by a static friction force?

Every body is affected by the force of rest. But if some other force is more important than the resting force, or the body has a small number of points of contact with the surface, then the body begins to move. Both the resting force and the rolling force act on the ball due to the smooth surface. In this case, the rolling force exceeds the resting force, so the ball begins to move. Also, the ball has much fewer points of contact with the surface. The rolling force does not act on the bar, since the body has angles due to which the bar is supported, which is why the bar remains on the table.