Unitary vs federal systems
In a unitary system, all significant governing power rests with the central government, which may delegate some administrative functions to local bodies but can revoke that delegation. In a federal system, power is constitutionally divided between a central (federal) government and constituent states/regions, each with their own guaranteed areas of authority that the centre cannot simply override.
Example 1: Nigeria has 36 states, each with its own governor, House of Assembly, and defined powers alongside the federal government. Which system does this describe?
This describes a federal system -- power is constitutionally shared between the federal government and the states, each with defined areas of authority, rather than all power being concentrated centrally as in a unitary system.
Presidential vs parliamentary systems
In a presidential system, the head of state and head of government (often the same person, the president) is elected separately from the legislature and serves a fixed term, largely independent of the legislature's day-to-day confidence. In a parliamentary system, the executive (prime minister and cabinet) is drawn from the legislature (parliament) and remains in office only as long as it retains the legislature's confidence/support.
Separation of powers
Government functions are typically divided into three branches: the executive (implements and enforces laws), the legislature (makes laws), and the judiciary (interprets laws and settles disputes). Separating these functions, with each branch able to check the others' power, helps prevent any single branch from becoming too powerful.