How to get over fear of public speaking? What causes this?

I have no clue why I respond so "violently" to speaking in public, i.e. speaking in front of a lot of people. The weird part is that I'm not shy. I can talk to anyone. I *am* introverted, but it is fairly easy for me to speak to someone if we have reason to be speaking or common interests. I can also fairly easily speak to strangers-- and my intonation is fine. I actually have a pretty loud-ish and clear voice, and when I'm comfortable with people, I would say I'm actually very good at doing whatever it is. Charades game with a ton of friends? I'll have a blast.

But speaking in front of a class, or in an audition for something (did one once)-- it is so uncomfortable that my hands literally shake. Like my whole body just trembles and it is very noticeable. I look as if I'm going to pass out (feel okay for the most part, except for some horrible feeling of dread)-- what causes this and how could I maybe fix it?

I've even done karaoke before-- I LIKE karaoke, and have been complimented afterwards, because I am loud and can at least carry a tune, but WHAT is with the shaking? I forgot to breathe once, simply reading something I wrote out loud in a writing class. I had to stop in the middle and apologize and confess that I had to breathe before continuing. Then when I'm instead faced with a problem in which there's a crowd of people and no one can get their attention, I am totally fine being that person to get everyone's attention and give some kind of instruction. It makes no sense to me that both of those situations would happen to the same person.