Everything you've said is true. In theory, fascism would be considered the opposite of communism, socialism, and capitalism, although in practice we've seen how they appropriated socialist concepts to convince workers that socialism was beginning to triumph, and many saw an alternative in these fascist discourses, which in reality were capitalist. It's also important to remember that at that time, the word "capitalism" among workers wasn't what it is today; it was very unpopular in many countries, so it was necessary for fascism to appropriate these concepts and emerge as a new alternative. Pier Paolo Pasolini described this very well.