What is Federation:
A federation is a formal and institutionalized grouping that welcomes various autonomous social entities around a common interest or element. The word federation comes from Latin foederatio, which means 'union'. Therefore, federation refers to the action and effect of uniting.
From the legal point of view, there are two definitions of federation: the first refers to the federal State, a sovereign political unit formed by the union of autonomous entities with specific competences protected by the national Constitution. For example, United States of America.
The second refers to the association of associations, which can cover the most diverse areas of interest such as sports, trade unions, industrial and agricultural production, banking, commerce, science and research. For example, the International Federation of Football Associations, better known as FIFA.
What is a federal republic?
In the political order, a federal republic, also known as a federal state, is one that is organized in a decentralized way from the association of political-territorial entities or states, which agree on a common project and, at the same time, respect of local autonomy in various matters.
Within a federal state or federal republic, political-territorial entities or states are called federated states. As a theoretical model of political organization, this arrangement is known as federalism.
Some paradigmatic examples are the Federal Republic of Germany and the United Mexican States. Each of these republics is made up of a federal district and several federated states. They can elect their own authorities (governors, mayors and councilors) and manage their resources autonomously, according to the parameters determined in each constitution.