Fascism and socialism are two varations on the same theme. They are both based on government control of the economy.
Absolutely wrong. Fascism is a political philosophy, not an economic philosophy. If a lot of historical fascist states have in fact imposed economic controls, this is an incidental characteristic not a defining one. The defining characteristics of fascism are:
1) Dictatorship
2) Either no elections or rigged elections
3) Suppression of dissent
4) Militarism
5) Extreme nationalism
A state with these characteristics is a fascist state. In theory, a state with these characteristics and a laissez-faire economy, or a state-owned capitalist one, would be a fascist state; the fact that no fascist state has ever had either of those economic arrangements is a meaningless coincidence.
A state without these characteristics is NOT a fascist state. If it imposes controls on the economy, that does not make it a fascist state.