Except that one cop or soldier here that claims you really aim for the head.
It depends on the drill. I am a Marine, and now a police officer. Different teaching, basically because as a Marine you use a rifle most of the time, and as a regular police officer you use a pistol. You only get a pistol in the Marine Corps if you're an officer, SNCO or your MOS requires one. Like a machine gunner will have one, so he has a backup in case his 240 goes down. Its also up to command discretion so others may get one too. So the vast majority of Marines do not ever get qualified with a pistol, or get issued one.
Center mass is generally what you are told to do, in both cases. Because you have more room for error, if you are off. The head is a much smaller target than the chest. There are also different drills. In the Corps we also shoot in the groin, it counts the same as a head shot. The head shot is really hard to hit, because its just a "T", not the whole head. Basically just above the eyes, and down to the mouth.
The Marine Corps now also has different tables in the rifle range, instead of there just being one. There are now four. It used to be that you just shot from the 200y, 300y, and 500y range (all iron sights btw). And that was it, qualified. Now there are ranges where you shoot while moving forward, do magazine changes while moving, and on your own. Face backwards, turn and shoot the target. These are all silhouette targets btw. Table four even has moving targets. All of this is done between 25m and 10m I believe. I've only done it twice, and only tables 1 and 2 are needed to be qualified. I did tables 3 and 4 before deploying as part of the workup.
In the latter tables there are different drills. Sometimes its two to the chest, or two to the chest and one to the head. Or a single kill shot. And then different still, a deliberate pair, and a hammer pair is two rounds in less than a second. Supposed to put someone in shock if hit in the chest. So when they say fire, you've got 3 seconds to raise your rifle, put it on fire, sight in, and shoot two shots in the chest. Sounds hard, but its really a lot of time.
Hmm, I kinda blabbered and went all over the place. Oh well.