Try this on for size:
Do you see how 'National' and 'Sozialistsche' are either one word or hyphenated? That will tell you that socialism is NOT a separate concept. It's National-Socialism, not National Socialism. I'd explain it further but you're quite simply not worth the effort
They literally didn't. Literally.
Do yourself a favour, please, and read the following article which explains it quite well, how the language was manipulated - no, not English - German.
Were the Nazis Socialists? | Britannica
Well, he is . . . and chico . . . and a few others