Sarik, the difference is the registration marks on the aircraft. While flying an N-registered aircraft, for instance, they are following the FAR's. This is common in cross-border traffic.
It changes when you want to fly an aircraft registered in another country. This is when you need to start satisfying the appropriate regulations applicable to the nation of registration.
As an example, when flying South African registered aircraft elsewhere on the continent, I required an SA validation (Air Law exams) and they also accepted my Canadian medical.
Now, in Nigeria, I required the same exams but also a Nigerian medical in order to get the validation.
Hope that helps.