I think of it this way.
* fill in - "in" means to fill (write) something "in that space". So it's appropriate for "the blank", which is a location.
* fill out - "out" means "completely", so it's appropriate for something more substantial than a single entry, such as a form.
So, "fill in the blank" and "fill out the form" are common an natural. "fill in the form" and "fill out the blank" are not, in my opinion.