The major difference between the economy under Stalin and that under a capitalist economy is Stalin's policy of state ownership of the means of production. This was an extension of his particular interpretation of communism. With initiatives like the Five-Year Plan and the collectivization of agriculture, Stalin essentially brought all vital sectors of the economy under state control, something that theories of capitalism reject.
In capitalist economies, the traditional approach is to allow ownership of production to rest in private hands with as little state intervention as possible. This is what is meant by the famous phrase "laissez-faire," or basically, "let the economy do what it will do." The belief here is that too much state presence stifles economic productivity and entrepreneurial imagination.
With communism, however, the belief is that private ownership of the means of production leads to the wealth of a select few, and the oppression and manipulation of practically everyone else. Hence, the idea behind state ownership is that resources and opportunities can be gathered together under a central authority, then redistributed as justly and evenly as possible.
Additionally, the socialist centralization policies of Stalin can be seen as a reflection of his view of Russia as a country that needed to modernize quickly. In his view, for Russia to survive and compete on a global scale, he had to expedite the process as aggressively as possible. For example, according to the Library of Congress, Stalin's Five-Year Plan "called for rapid industrialization of the economy, with an emphasis on heavy industry." Again, in ideal terms, this is something that capitalist theorists would systematically reject as a proper solution.