Simply put, Marxism is a philosophy and communism is the ideal state achieved when Marxism is lived out. A Marxist is a person who embraces the philosophy of Karl Marx; a Communist is a person who applies Marx’s ideas to the government and the economy.
What did communism lead to? 61 million deaths in the Soviet Union, 38.6 million in China, two million in Cambodia (then called the Khmer Rouge), 1.6 million in North Korea, and 1.2 million in Yugoslavia.