No. They are not equal and neither same. If you understand Italian I suggest you to search for Prof. Barbero videos on the topic. They are quite better than anything I'll be able to convey.

Fascism:

It's an authoritarian dictatorship happened between 1914 and 1945 in Italy. The fascist regime and ideology was strictly based on Mussolini's figure, people marched in straight lines down the streets, everyone wearing the same uniforms and Italy was a great imperialist nation (lol jk it wasn't but they quite believed it). Fascism and the fascist party stopped existing after partisans overthrew the regime. Fascism is a 20 years long dictatorship. After that there were some regimes around the world that were inspired by Mussolini such as the current ruling party Italy Fratelli d'Italia, Marine le Pen's party in France, those shitty AFD in Germany, orban's Regime, franco in Spain etc etc. They are called neofascists, because Fascism was a 20 years long regime happened in Italy between 1914 and 1945.

Communism:

Communism is a model of governace that's never been achieved in human history, as someone above said it's about classless, stateless, governance models. It's been around for like 200 years (the Communist Party Manifesto is from 1848), and in every country of the world there is/ has been a Communist Party and as we know they were always persecuted for being communist, stopped from going to the government and stopped from bulding a classless society when they managed to get to govern. Just see what the USA did in the last 50/60 years in every country that risked a communist government: Chile and latin America in general, Italy and so on an so forth.

Fascism =/= communism, and if you say the contrary you just don't know how they work.