Multinational organizations are headquartered in one country but have direct operations in multiple nations. They tend to operate in a centralized and top-down nature with the corporate office calling the shots and subsidiary operations abroad fulfilling initiatives as best suits their local markets.
Multi-domestic organizations are nearly the opposite. They have operations in multiple countries, but they are highly decentralized. Local offices have a lot of discretion to make decisions and implement them. The rationale behind this is that local talent usually has the best understanding of their market.
Global organizations operate most widely around the world. Although they may have subsidiaries in different countries, operations and branding vary very little between them. Unlike the other organizations, global organizations have no single headquarters. Local subsidiaries run autonomously handling local matters, and the parent company deals with issues that pertain to the company at large.
Transnational organizations are the least centralized in a large respect. These organizations have no centralized base of operations. There may even be multiple bases for a single transnational corporation in each country in which it operates. Each individual operation is free to make its own decisions based on its localized needs.