Fascism just means "communism that I don't like." The full name of the Nazi party was the National Socialist German Workers' Party. When people tell you they are socialists, you should take them seriously.
counter point: our understanding and definition of socialism is dominated by Marxist socialism.
Prior to Marxism dominating this term, socialism was a spectrum of Catholic distributism, agrarian communalism, Fabianism, etc,
Tying the Nazi's to Marxist socialism is nonsense since Germans genuinely,
genuinely, despised the Bolsheviks. Don't forget, there was a failed Bolshevik revolution in Germany post WW1.
Many rightist parties saw swelling support against Marxism because of this failed revolution, the Nazi's included.
Caveat: contemporary German politics did point out this seemingly paradoxical name of the
Nationalist Socialist German Workers Party and it was ridiculed.
In practice, the Nazis had a mixed market command economy downright identical to what King FDR was doing, but I consider FDR a stalinist FAGGOT so in the end the interwar economies of all the major powers were
all shades of liberal socialism, nationalist socialism, and marxist socialism.
Caveat two: This is not an endorsement of socialism of any stripe, merely an attempt to delineate between very real strains of it that are diametrically opposed to each other.
tl;dr Socialism is in the Nazi's name but Democratic is in the name of North Korea and Red China. Not all socialism is Marxist.