Wrong, that was when the terms and definitions where created.
They can and have existed without the term or definition.
Hope this helps.
Fascism as a structured centralized power to serve mutual benefit of a people defined by allegiance to a national identity rather than subjugation by a self-serving autocracy/monarchy, exists at least as far as the foundation of the Roman republic and more likely has its most distant roots in the temple economies of the bronze age and hence as much as 5000 years past. Communism, as a classless society with communal production and distribution, has never even been attempted until the 20th century and then only existed with obviously inherently unstable approximations
20th century fascists were in an ideological feud with the nascent communists, who were driven by new, revolutionary and untested ideas. Fascism already existed throughout history and has competed with monarchies in several civilizations, and some societies drifted between the two as power was more centralized and removed from the people and in others served the people and their barons. The closest thing to communism to ever exist before Karl Marx is some isolated island tribes and even there its usually the biggest maori eats his rival and bangs his girl