Whereas the snatch is a pulling exercise—you feel it most in your back and grip—the jerk uses the pushing muscles: the triceps, shoulders, chest, and most of all the quads.
The jerk also demands a more exotic technique. Sure, the snatch also improves enormously when you cultivate better technique, but you’ll probably find the process pretty intuitive. You’re just doing two simple things, absorbing the momentum of the falling bell and lofting it back upward gracefully, and your body gets the feel quickly. But the jerk demands things that feel terribly unnatural.
First, you have kettlebells constricting your rib-box almost non-stop. You can’t breathe normally, and instinctively that is uncomfortable and frightening. (This is a big reason why people dislike long sets of barbell squats. And surf torture, too. In my experience, we don’t hate the cold as much as we think. What we hate more is actually how we instinctively tense up in cold water and breath in choppy, panicky gasps.)
Second, you bend backwards at the hips. Note that I say the hips, not the back. Only bend back at the hip flexors. That’s hard. And it doesn’t make breathing any easier. You’ve stretched your abdomen taught, loaded kettlebells onto your chest, and jammed your elbows into your belly. So what’s left to breathe with? Your upper back! To quote my old taiji teacher, “Suck in your chest and spread out your [upper] back” (含胸拨背). That way you can breathe into your back, so to speak, with your upper back rising and falling instead of your chest or belly.
You’ll need to relax your trapezius muscles. The more you relax them, the easier it all gets. You relieve some of the prolonged muscular tension, and better still, you can slide your elbows down your trunk to your hip bones and rest them there while you catch your breath. People who are really flexible and have good proportions—which is not me—report that they can relax fully in this position. Damn them!
The more you master this technique, the more the jerk becomes a leg exercise. In effect, you jump in place, bucking the bell straight up, and you only use your arms to catch them. Then you jump a second time to meet the falling bells in mid-air. Relax (if you can), breath, and repeat.
More than the snatch, the jerk builds muscle. The reason might be “time under tension” (TUT). Many coaches and researchers treat muscle growth as a function of “time under tension”—how long you’re under a heavy load without setting it down. Certainly people grow lots of muscle from heavy high-rep barbell squats and Javorek complexes, which are two very different things, but in both cases you stay under great tension for a vomitously long time. Jerks do the same. You spend 10 minutes under an awkward pair of cannonballs totaling 32kg to 64kg (70-140 lbs). (Imagine front squatting or back squatting one of those poundages to a high box for 10 minutes. Now, don’t actually do that (!!)—you’d lose form, making it unsafe AF. But you can imagine what a metabolic supercharger that would be.)