In my own opinion/definition, I might say a twitch is milder or confined to a smaller area of your body and a jerk might be a bit more powerful and incorporate movement from more of your body if not your whole body. But my experience with these, as they pertain to kava consumption, is that they are sudden, random, occasional, single movements. It's not repetitious, long lasting or predictable. A single quick involuntary spasm is all.
As for other kava related 'movements', I've read reports of people drinking too much kava in Vanuatu, which is typically quite strong, and when they've had too much, their body trembles for some amount of time, until it wears off. On occasion, certain kavas or doses, or drinking root too soon after drinking liquor will sometimes give me an anxious-tremor feeling which subsides after about 20 min. This is more of a quivery movement, like shivering.
I've also read a rare report or two that kava was believed to cause 'parkinson-ism' in certain individuals...this is likely a rare genetic issue that a very small minority of kava drinkers might face...it may also require kava + (unknown medication) to occur. Who knows. I also recall reading warnings in the past that people with Parkinson's disease shouldn't drink kava. In my own experience with something similar to this, I made a strong batch of kava once and drank it with a friend who typically drinks alcohol, after a few shells, her head began to sway back and forth slowly beyond her control. It was transient in this case and didn't persist. But if you're having persistent involuntary motor function issues that seem to be related to kava, I'd stop for a while to see if it subsides, consider any other medications you may be mixing with kava that could be causing it and perhaps quitting kava altogether if appears to be the sole cause. You definitely wouldn't want to provoke any neurological issues you might personally be susceptible to.