쥐다 is closing your hand around something: a spoon (왜 숟갈을 그렇게 쥐니), a shoe (자기 신발을 벗어서 이렇게 쥐고 있는데), or your own fingers into a fist ([다소 앙증맞은 계주먹] 이렇게 쥐는 사람은). Squeezing and releasing is 쥐었다 폈다. Watch the compounds: 쥐어 패다 is beating someone up (제일 세게 쥐어 패고 싶은데) and 쥐어 짜다 is wringing something out, including wringing an answer out of your own head (어떻게 쥐어 짜봐). 잡다 is holding or grabbing generally; 쥐다 is specifically in the fist.