Slingshot is a modern toy made from rubber, and can be used to hunt small game (small rodents and birds at ranges up to 25 metres according to wikipedia). "A typical heavy pull band slingshot should be used with 9mm (3/8") to 12mm (1/2") steel balls."
Sling is an ancient weapon, more accurate and able to fire farther than the bows Persians used against the Greek. I don't know whether the Greek used leaden of stone ammo against the Persian archers. Bow technology evolved until bows had completely replaced slings as weapons of war, excluding the use of the same mechanism in staff-slings and in siege engines such as trebutchet, in the Middle Ages. "Almond shaped leaden sling-bullets were typically about 35 mm (1 3/8 in) long and about 20 mm (3/4 in) wide."
Also, I can hit a small tree with a slingshot, if I'm close enough. I can hit a barn with a sling, but if I'm not far enough the stone will ricochet and hit me in the head.