I am watching History International, and there is a show on about the battle of Masada. They just mentioned that the Romans had Syrian and Arab slingers, and that the Hebrews had slingers as well. It also briefly showed how deadly they are, and were used as a mobile, high accuracy at close range weapon. They did not define close range, but I assume it was in comparison to the siege weapons they had in the camps.

Probably, the distinction between slings and arrows on the one hand, and spears and javelins on the shorter end of the ranged weapons.  N/M ballistas and such for now, though the onager was sort of a megapower staff sling.  Arrows were pretty accurate to between 200 and 300 yards, generally fired in a high arc, not flat like at a target.  Slings were the same, but we know they could outdistance arrows.

Remember that the armies then fought in massed groups.  You didn't have to aim at a particular person, just hit in the crowd to do your damage.