Actually in many cases, foreign students who come to the US to train actually train to foreign standards here, using instructors who hold foreign CFI qualifications. They will also complete at least some of their FAA ratings in parallel, since they need those to fly solo here. Many complete all of their FAA certs just to have them...might as well.

A few third world countries merely require that pilots hold a license issued by the FAA, JAA, CAA, etc. Others may issue you a local license based on possession of an FAA, JAA, etc. license.

Canada and US are very similar. JAA is tougher. Maybe someone with specific experience can chime in about actual third-world training specifics.