I don't know English very well but in my experience in the US fill out is used mostly in fill out a form or application. Fill in is used in fill in a blank or empty space or when a player is injured another one is selected to fill in the position.

Yes, that's right. I think you can hear both forms in the US but Brits almost always say fill in, not fill out.

They both mean the same thing. In America, both forms are common and used interchangeably. But I can't say the same for Britain because I don't know.