In General, the coversion of professional licenses from any country to any other requires at minimum one or more written exams and one or more flight tests. Some countries will simply allow a license to be processed over paperworkwise for Private, non-commercial, recreational flying. One or two might even take your FAA certificate at face value, but these are few and far between. Of course, as you accurately have observed there are N-registered aircraft flying workwide and all you need for those is the FAA Certificate.