A punch (or hard stroke or whatever you want to call it), or a forceful but slower stroke at the same contact point on the cue ball will cause the cue ball to slide more and then draw. Most people who grip the cue to tight or don't have a very good stroke in the first place tend to do the latter automatically. However, this type of stroke can be used as a tool in ones game. I personally hold the cue fairly loosely and have quite quick cue speed. I tighten my grip and paused on my backstroke for these type of shots because of this. Its much easier for me to achieve consistent results this way. The speed of the cue has changed in these instances but I'm now relying on the mass of my arms to punch into the cue ball, rather than "throw" my cue through the cue ball with nice unhindered pendulum action.
For practical purposes there are four and only four things that determine everything about how the cue ball reacts (everything about the speed and spin). They are:
1. Where you hit the cue ball.
2. The speed you hit the cue ball.
3. The elevation of your cue.
4. The weight of your cue.
So when thinking about or describing a shot, those four things (well really only the first three since the weight of the persons stick can't be changed for a shot so usually no need to even mention it) are all you need to think about or describe when explaining to someone how to hit the cue ball on a particular shot (and number 3 is generally assumed to be "as level as possible" unless stated otherwise so you usually don't have to mention that one either, which leaves just the where and at what speed).
Anything to do with grip, wrist, poke or smooth stroke, or anything else like that have zero affect on the cue ball (unless they affect one of the above things like making you hit the cue ball in a different place than you intended or think did because of a certain grip that changed your impact point for example). So in describing your shot above, all you really need to tell us was where you hit the cue ball and at what speed. The rest of the stuff makes no difference. All the cue ball knows is where it was hit, how hard, at what angle, and with what weight of cue.
If a "punch" or certain length of back stroke or how tight your grip is or any of that is having any affect on how your cue balls reacts it is only because it is changing where you are hitting the cue ball or how hard you are hitting the cue ball.