No. Socialism is when the government owns the means of production.
Communism is when the people own the means of production.
Fascism is when the government directs privately-owned production.
Sorry. The definition I use is directly from a 1967 websters. If the commies have managed to rewrite some of the dictionary since then, I don’t accept it.
Same dictionary defines capitalism as privately controlled production and distribution.
It defines fascism as a system of gov characterized by dictatorship, belligerent nationalism and racism, glorification of war, etc. (sic).