Careful! There is some variation in usage of this term, so you need to make it clear which way you are using the word. First, a "push out" is something very different from a "push shot". At nine ball, the first shot after the break can be played as a push out if declared in advance, and the requirements of ball and rail contact are waived. The incoming player can pass the shot back to the pusher. At pool, a push shot involves a very special kind of stroke and is played when the cue ball is frozen to the object ball -- this stroke is a foul. (At pool it is legal to shoot towards a ball the cue ball is frozen to, assuming no other foul, and with a normal stroke.) In a push shot, the tip is brought slowly, slowly, very slowly up to the cue ball until it is just touching or about to touch, and then the tip is accelerated for the shot. Two examples: 1. A ball is frozen to the rail close to a corner pocket. The cue ball is frozen to the object ball and straight out from the rail. The shot is straight towards the object ball, with the tip placed on the equator of the cue ball with lots of side away from the pocket. Once very gentle contact of tip-to-ball is made the tip is gradually pushed forward and the object ball sort of slips out from behind the cue ball and goes straight into the near pocket. 2. The cue ball is on the foot spot, and an object ball is frozen as if it had been spotted; both are on the foot string. A desirable object ball is in the jaws of one of the foot pockets. A legal way to pocket the hung ball is to point the cue stick at a point on the foot rail half way between the center of the rail and the target pocket, and shoot a normal center ball stroke. An illegal push shot is to elevate the butt of the stick to about 45 degrees, address the cue ball for extreme follow, and shoot a gradual push shot. In this case the cue ball will nearly ignore the object ball, and go close to the line of aim, rather than the double "angle" of the first (legal) method. At pool, when the cue ball is close to but not frozen to the object ball, and the cue ball is shot straight at the object ball with a normal stroke, usually a "double hit" occurs. This is a foul. At snooker, you are not permitted to play the cue ball towards a ball it is frozen to, nor to play double hits. At carom billiards, "push shot" includes any shot where the cue ball is close to or touching the object ball and the shot is a foul.