To yank is to pull violently / roughly. To pull is a neutral word, simply meaning an action, e.g. I pulled the door handle. The normal meaning of the verb twitch is a sudden, sometimes involuntary movement involving a part of your body, e.g. my leg twitched. It doesn't normally involve another object.

Did you mean twist? A yank is a very hard and sudden pull. A twist is taking something and turning it. Usually the thing you are twisting is fixed at one end. When you turn it, it can form a shape like a corkscrew. If you hold one of your own fingers and turn it - this is twisting.

A twitch is like a nervous tic. It's like when you're smiling for the camera, you try to hold that smile forever and the muscles around your mouth want to do a tiny spasm or movement. That's a twitch. 'Yank' and 'pull' are the same, but when you 'yank', you are doing it much more vigorously and sudden.