The two principles mentioned are actually interconected. The power in a state is divided in three brances: legislative, executive and judiciary. This is the separation of powers. Moreover, in order to ensure that each of the branches does not exceeds its functions, a system of checks and balances is implemented so that each branch supervises the others.
Separation of powers:
- The Judicial Branch interprets the law.
- The Executive Branch has the responsibility to carry out the law
- The Legislative Branch makes the laws
Checks and balances:
- Congress may impeach judges and the president
- The president can pardon persons convicted of a crime.
- The court has the power of judicial review (to declare laws unconstitutional).
- Congress can override a presidential veto by a 2/3rds vote in each house.
- The president appoints federal judges