what are the similarities between monarchy and republic
Answers
There can be many similarities between a republic and a monarchy.
First, they can have a different head of state and head of government. Germany is a republic where the head of government is held by the Chancellor (now Angela Merkel) and the head of state is held by the President (now Frank-Walter Steinmeier). The United Kingdom, is a monarchy where the head of government is held by the Prime Minister (now Theresa May) and the head of state is held by the Monarch, Her Majesty Queen Elizabeth II (since late 1952). Both countries adopted parliamentary system.
Second, both can be a democratic country or an authoritarian country. Japan is a democratic monarchy, the Emperor does not have (or have limited) control and intervention on its foreign and domestic politics. On the other hand, Brunei is an absolute monarchy where the Monarch practically has control over anything.