Yeah, Socialism and Capitalism exist on an the axis of Materialism, where the left is more socialist, and the right is more capitalist.

Mussolini's vision of Fascism was a strictly corporatist one, however, it's unfair to assume that all Fascists would embrace such a system, or especially that all who embrace such a system are Fascist.

The fasces in American symbolism have nothing to do with Fascism; fasces where used back in Ancient Rome — and even earlier than that — to symbolize law and order. This is why it was adopted by Fascists, but it's also why it was adopted by America, the difference is how the two view law and order.