The word 'snap' does indeed have a variety of uses, but what links them all is this : a sudden quick movement, with a burst of noise.
It can mean opening, closing, breaking, taking a photo, suddenly speaking angrily, or clicking two fingers together. There's even a card game called 'Snap' where you shout 'Snap!' and slam your hands down on the table when you spot the same two cards in a sequence.
Versatile little word, isn't it?