I received a question from a Billiards Crossing member and as I recalled, this is often contentious issue, so I thought I would go at it from a couple different angles. (Lousy pun). 

What is a definition of a push shot?  Can you have a push shot when the cue ball is two to three inches away from the object ball with high english? 

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. Here's an example: 

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. 

The legality of this shot depends on whose rules you are playing under. There are local sets of rules that declare any kind of push shot which involves shooting a object ball frozen to the cue ball as illegal.

It is topic of considerable interest, a discussion of this issue evolved overnight on the Inside Pool and Billiards Forum: My understanding is, if they are frozen ! It would be considered a "PUSH" shot and illegal if you try to shoot with a normal forward stroke ! I usually shoot those balls with elevated butt and the same as if I was using a Masse~ on the cue ball or in other words similar to a "throw" shot!--Phil 

If the balls are frozen, you can shoot your normal stroke in any direction. If they are not frozen, but very close, you probably need to shoot at an angle. Most players think that shooting down on the cue ball gives them a free pass on this shot. This is not the case. The problem when the balls are very close is that it is very likely the shooter is going to hit the cue ball twice. When they are actually frozen, this should not be a problem. But you must use a normal stroke to avoid pushing the balls as Phil mentioned.Steve

Steve resolved the question by pulling out the BCA Rule Book: This is straight from the BCA rule book"

3.23 FOULS BY DOUBLE HITS
If the cue ball is touching the required object ball prior to the shot, the player may shoot toward it, providing that any normal stroke is employed. If the cue stick strikes the cue ball more than once on a shot, or if the cue stick is in contact with the cue ball when or after the cue ball contacts an object ball, the shot is a foul. (See Rule 2.20 for judging this kind of shot.) If a third ball is close by, care should be taken not to foul that ball under the first part of this rule.

3.24 PUSH SHOT FOULS
It is a foul if the cue ball is pushed by the cue tip, with contact being maintained for more than the momentary time commensurate with a stroked shot. (Such shots are usually referred to as push shots.)