America and the USSR didn't physically fight in fear of destroying the world with nuclear weapons 
That didn't necessarily mean there were no deaths or wars involved, physical and mental. 
Overseen by Presidents: Harry S. TrumanDwight D. EisenhowerJohn F. KennedyLyndon Johnson Richard Nixon Gerald FordJimmy CarterRonald Reagan George H.W Bush 
What's a communist mom?
Red Scare
That lady's a bad, bad person
She's wearing red, she's a communist!
People were randomly accused of being communist with no actual reason or evidence. They often lost their jobs and social standings
Call the Police!
Berlin wall
West Berlin was Capitalist while East Berlin was Communist. People from West Berlin often enjoyed life more while the people in the East were treated less than dirt. People from the East were shot while trying to flee and a wall was built to attempt to stop them.
Vietnamese war
Fought between the communist North Vietnam and the Capitalist supported Southern Vietnam and one of the longest wars in U.S history. The U.S ended up losing