The US government consists of three different branches. This includes the legislative, judicial, and executive branches. The legislative branch consists of Congress, who is in charge of making federal laws. These are laws that all citizens are supposed to follow. The judicial branch consists of the Supreme Court. The Supreme Court is tasked with interepreting what the Constitution means and what rights are protected under the constitution.
Lastly, the executive branch consists of the president and their cabinet. The president is supposed to be the leader of the US and is tasked with making important decisions regarding America's foreign, domestic, and economic policies.
Both nations did not want to fight directly because of the threat of a nuclear Holocaust, They were the most powerful nations that spread influence and dominance to surrounding countries and fighting them directly would have started another World war.