In my opinion, an important detail that perhaps hasn't been mentioned yet is that it's not about only using pinpoint targets or only using zones. You should utilize both during the thinking process.
What I mean is, you should first figure out which shot gives the best zone to work with for your cue ball, just like Tin Man and others have talked about in great detail already, but when you have decided on a zone, you should then pick a point within that zone to aim at that gives the best results on average for your specific situation, and that point becomes your final aiming target. When you are down on the shot, you don't think about the zones that lead you to aiming there, you only think about the end-result, the singular point.
Most commonly, this ideal point to aim at should be within the middle point between going too short and long within a zone. But sometimes it's not, for example, you could have a zone where you have a shot for a 2 diamond long distance, but the first 1.5 diamond distance leaves a much tougher shot than the remaining 0.5 diamonds.
Let's say your realistic scatter in terms of power for this particular shot is +-0.5 diamonds. Or in other words, 99.9% of the time you will land within 0.5 diamonds either way of your target point power wise.
You now have two simple options, aiming at the center of the entire 2 diamond zone of having a shot, or aiming at the center of the 0.5 diamond zone where you have ideal shape.
1. Center of the entire 2 diamond zone. This would leave you with the tougher shot 100% of the time (from 0.5 to 1.5 diamonds with scatter).
2. Center of the smaller, ideal zone. This would leave you with a 25% chance of a tough shot, 50% chance of an easy shot, and a 25% chance of no shot at all (from 1.25 to 2.25 diamonds with scatter).
Neither of these are the ideal target.
You should skew the middle point slightly towards the easier edge to increase your odds of hitting the ideal zone for an easier shot, just not too much that you start risking missing the 2 diamond length zone altogether. Picking the 1.5 diamond point as your target (from 1 to 2 diamonds with scatter), you would have a 50% chance of leaving the harder shot, and 50% chance of leaving the easier shot.
If we use the same shot as an example, but change the person playing and say that their scatter for power is 4 diamonds instead of 0.5 diamonds, the ideal target point becomes the middle of the entire zone of having a shot at all. Or if the person has a scatter of 0.1 diamonds, they should aim at the center of the ideal 0.5 diamond zone. It's all about your scatter, and being realistic about it. Overestimating your abilities will only hinder your odds.
So, to put it all together, first pick a zone. Then think about the value of landing on all points along the zone in terms of power, and how large your scatter is. Then pick a singular point target based on those factors as a final aiming point.