The First Red Scare happened after the Bolshevik October Revolution of 1917, that lasted from the late 1910s to the late 1920s. It lead to an increased fear and perceived threat of revolution and political radicalism from national and foreign anarchists and from the American labor movement, which is mainly leftist.
The Second Red Scare happened after the Second World War, during the start of the Cold War, that lasted from the late 1940s to the mid to late 1950s. It led to a fear of national or foreign communist spies infiltrating and taking over U.S. society, institutions and the federal government. The Second Red Scare is known as McCarthyism.