My personal experience...one can get busted for target shooting with anything. According to the national forest (cleveland) representative, he can write me a ticket for using a sling shot. He gave me a written warning for target shooting with bow. I was merely checking my pins for accuracy prior to a rabbit hunt using blunts on a broad head target block.
Per Nicapopolis post: San Bernardino states "Discharging a firearm, air rifle, or gas gun, except for the lawful hunting..."- That specifically states air rifle.
So from my understanding (now)...Target shooting is what ever the authority deems it to be as long as you were not in pursuit of game.
What a hunting license affords you is shooting at a piece of dirt 50 yards because you think there was a rabbit there. Piece of dirt, not a piece of paper that says "target"!