Your characterization sounds accurate. Usually you fill out forms. (Note you “sign” them if that is the only thing requested) Please fill out this health history before seeing the doctor. (A type of form) You need to fill out Schedule A. (A tax form) Note that it’s also very common to use “do” instead of “fill out”, especially if the form is electronic and not paper. We have to do our taxes. My son’s finally getting around to doing his college apps. “Fill in” would be part of a form or something short. I didn’t know what to fill in for #7. You can leave the rest blank, but fill in your insurance information.

Thanks for sharing your point of view

Personally, I wouldn't say "fill *in* this form. I think Trung's logic about filling out *the entire form* versus filling in spaces/blanks is sound.

They mean the same thing and are used interchangeably. For example one can say: "Will you fill in this form please? or "Will you fill out this form please?"