The rule of law means no one -not even the monarch, is above the law to prevent arbitrary power, promote democracy and protect the rights of the people.

I. 1689 UK and 1787 US : new political regimes (docs 1, 3 & 4)

1. Political regimes

  In the UK In the US
Head of state = A king or queen who inherited the crown
= a hereditary monarch.
The current monarch is Queen Elizabeth II (the 2nd)
= An elected president.
Today, the current president is Donald Trump
=> Political regime A monarchy = a political regime in which the head of state is a hereditary monarch. A republic = a political regime where the head of state is an elected president.

2. The separation of powers

  In the UK In the US
The executive power
(the executive)
implements the law
held by the monarch
in Buckingham Palace
+ the Chief Minister (Prime Minister = PM)
in 10 Downing Street
+ the Cabinet (government)
held by the president
in the White House
+ the vice-president
+ the government.
There is no PM in the USA
The legislative power
(the legislative)
makes law
held by Parliament
in Westminster Palace
= House of Lords : hereditary Lords
+ House of Commons : elected MPs (members of Parliament)
held by Congress
in the Capitol
= Senate : elected Senators (Sen.)
+ House of Representatives : elected Representatives
The judicial power (the judiciary) applies law held by the High Court held by the Supreme Court

=> Both the UK and the US respect the separation of powers. Each power (legislative, executive and judicial) is held by a different player (individual or institution) separated to prevent dictatorship, abuse of power and respect the rule of law

3. The balance of powers
In the UK, the 3 powers are unbalanced as the legislative is stronger than the executive. It means that the monarch is controlled by Parliament, that royal power is limited which defines a parliamentary monarchy.
In the US, the powers are balanced because the executive & legislative are equally shared. Besides they mutually control, check one another. It is the principle of checks and balances

4. The sovereignty of the people
The sovereignty of the people means that legitimate power comes from the people, that the nation is the basis of power
In the UK the people is represented in Parliament as they elect the House of Commons and the nobility sat in the House of Lords.
In the USA the people elect members of the 3 powers : President, Congress and judges

II. UK’s parliamentary monarchy and US republic today (+ docs 2 & 5)

1. Democracies
Democracy is the government of the people, by the people, for the people
Today both the UK and US are democracies as everyone votes thanks to universal franchise.
In 1689 and 1787, however, they weren’t democracies because the franchise was restricted to wealthy people. Moreover, in the US African-American (Black) slaves didn’t have the right to vote.

2. The Queen’s role
In the UK today, the monarch is still the head of state but no longer has any real/actual power. The prime minister (PM) governs and keeps the monarch informed but it is only a tradition not an obligation. For example, in 2016, when David Cameron resigned and Theresa May became PM, it became official after their visit to the Queen.
The Queen, however, is a major symbol of stability because she is above politics : she doesn't express any political opinion. She is also a strong national symbol : she unites and reassures the British in times of crisis like the 2016 Brexit.