The meanings are all related. "White" means, in the United States, "part of the majority culture". If you're not white, you're reliant on the legal system to protect your rights as a minority. If you're white, it just happens -- your rights aren't in question in the first place.

"White privilege" is simply the "privilege" of being treated with a baseline of respect and decency. It's NOT, actually, a level of respect ABOVE what people ought to be able to expect -- rather, it's the "privilege" of being treated the way that people ought to be treated in general. It means the "privilege" of NOT being subject to persecution.