Country A
Local and state government share power with the central government
The central government has final authority.

Country B
Local and state governments share power with the central government
The state governments have final authority.

What types of government do Country A and Country B have?
A. Country A: Confederation, Country B: Federation
B. Country A: Federation, Country B: Confederation
C. Country A: Parliamentary, Country B: Unitary
D. Country A: Unitary, Country B: Parliamentary

A federation is an institutionalized grouping of relatively autonomous social entities. The federation is usually associated with the formation of states formed in turn by the meeting of several territorial and political entities. It is also often referred to as the federal state or federal republic and generally has a republican and exceptionally monarchical political system. The term is opposed to the unitary or centralized state.

A confederation consists of the union of states that retain their sovereignty and are governed by certain common laws. The word confederation takes much more relevance when it comes to a permanent alliance of States or some association or commonwealth of States. In terms of modern politics, it is a permanent union of sovereign states for the purpose of common action. It usually originates through written agreements, and then establishes specific norms or laws that regulate and govern this link. Confederations are usually formed to address issues of a greater nature, such as defense, immigration policies, the creation of a common currency, the fight against poverty, social integration, etc.