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A punch involves the closed fist and punching with the fore-knuckles, i.e. karate punch, and a strike involves the open hand such as a slap to the head, an open handed back hand to the face, or the use of the open hand, the elbow, the forearm or both elbow and forearm.
Use the strike to hit a target, pass beyond to a possible additional attack or block or parry or back to a defensive position, etc. No wasted motion and it should be followed by another technique, don't just to a ippon kumite move by stopping and expecting it to finish the job.
Both the punch and strike may be used as a prelude to your overall goal of stopping the encounter as quickly as you can. You may punch to open a path to a disruption of their structure and balance or a strike to move yourself into the next step of your overall multiple processes to stop the encounter, etc.
This leads to the maxim in martial arts of hard/soft-soft/hard. Marc MacYoung on the Animal list asked me if I knew what he meant and then at my request elucidated. It means use a hard, fist, against soft targets; a soft, strike/slap, against hard targets.
Know this, if you think your makiwara training along with tameshiwara will condition your fist, knuckles, fingers, bones of hand against breakage when you hit a hard bone then think again. The punch is best used against those vital points that are the weak, cracks in armor of body, points of the body while using an open hand against those hard targets, i.e. face, so you don't break your hand. It is worth the time and effort to research this maxim and incorporate it into your training and practice.
I advocate the use of both makiwara and heavy bag. Both serve a purpose in teaching a person how to apply powerful techniques and those training tools are invaluable to that goal. It is worth the time and effort to search out and find those training examples for both if your martial system is a fighting system, i.e. not sport, not tournament, but school yard or street type fights (to a point because violent predatory stuff is another ball game altogether!)
p.s. It was interesting to hear the definition of Mr. MacYoung's reference to punch and strike because I remember using both in sparring, etc. over the years as an instructor yet never heard that maxim till now. Always learning something new and exciting.
Sutrisno, Tristan, MacYoung, Marc and Gordon, Dianna. "Becoming a Complete Martial Artist: Error Detection in Self Defense and the Martial Arts." Lyons Press. Connecticut. 2005.