When and why is the word "transnational" used instead of "international"?
According to Wikipedia entry 'Transnational organization', transnational refers to international organizations that TRANSCEND the idea of a nation-state. Thus, the word emphasizes that national boundaries are not relevant, which was what Trump implied, how crime organization ignores national boundary when it comes to their operations.
International, however, implies official cooperation between countries, and respecting the law of the nations involved.
Hope that helps.