Great Britain has a monarchy, which means it has a king or queen, but they mainly just do ceremonies while the real power is held by elected officials called Parliament. In contrast, Germany is a federal republic, which means it has a president as the head of state and a chancellor who runs the government, and both are chosen through elections.
Both countries have a system where people can vote for their leaders, but Great Britain's government is more focused on tradition with its royal family. Germany has a stronger emphasis on a president and a chancellor working together to make decisions for the country.