All anemones kill and eat by paralysing the food. Their tentacles shoot spear-like nematocysts into the flesh of the pray, injecting a toxin. To a small creature, it'll be killed by it. The tentacles stick to the fish (as it's got spears into it) and draw the food to the mouth.
For people, anemone stings are either a small tingle if it's on the back of your hand/soft skin, or for more powerful anemones like tube anemones, carpet anemones (including mini-maxis) it can be like a bad nettle sting.