Marx’s definition of socialism is unhelpful, has been detrimental, should be ignored. He did advocate for socialism, but in a specific way. He saw socialism as a step towards communism. Marx believed that after a workers’ revolution, society would first enter a socialist phase where the workers control the government and economy. Then, eventually, this would lead to communism, where there would be no need for a state and everyone would share everything equally.
The United States regulates businesses, provides welfare. Those are socialist ideas. China, controlled by the Chinese Communist Party, has rich and poor people. It isn’t communist.