1) They are BOTH SOCIALISTS
Is there a nobler or more excellent kind of Socialism and is there a truer form of Democracy than this National Socialism which is so organized that through it each one among the millions of German boys is given the possibility of finding his way to the highest office in the nation, should it please Providence to come to his aid.
A Hitler(January 30, 1937).
2) BOTH backed-up by the American Super-Rich
3) BOTH used STORM-TROOPERS to quash political opposition. The Germans has the BROWNSHIRTS, the Democrats have ANTIFA and BLM.
4) BOTH employ "social justice" as an argument for criminal theft.
Because it seems inseparable from the social idea and we do not believe that there could ever exist a state with lasting inner health if it is not built on internal SOCIAL JUSTICE, and so we have joined forces with this knowledge. Adolph Hitler
5) BOTH practice the politics of RACIAL IDENTITY.
There are far more similarities than you mentioned. Both the 1930's Nazis and the modern Democrat Party used violence as a tactic to silence opposition, they both sought to deprive their opposition of their basic human rights, they both used a fake victim tactic of repeating a false narrative of being victims of the opposing parties, they both practiced historical denialism and revisionism, they both used the justice system to stay in power, they both used abortion and eugenics to rid the country of undesirable racial elements.
They both used the media and movies to dehumanize their enemies (Jews, conservatives), they both were anti-Semitic, they were both warmongers, They both wanted socialized health care and put doctors on low salaries, they both created a shitload of government jobs, they both indoctrinated the youth with their agenda and beliefs, they were both staunch advocates of gun control, they were both shameless exponents of identity politics.
They were both propnents of nationalization of business, forced profit sharing, outlawing all profits during wartime, abolition of all income not earned directly from work (via high capital gains/inheritance taxes). They both believed the state should provide a "livelihood for its citizens", old age insurance funded by government, price caps, price controls, rent controls, laws against speculation,"communal" rent free living areas, an end to the "materialistic" world order, free higher education focusing on "civic affairs", humanities, and political science. They both used censorship against news media that don't tow the line, believed in the "common good" and "common interest" before individual interest, and a strong central government to make these goals come true, mainly through economic coercion and force.
Adolf Hitler said it himself in a speech he made in 1927:
"We are socialists, we are enemies of today's capitalistic economic system for the exploitation of the economically weak, with its unfair salaries, with its unseemly evaluation of a human being according to wealth and property instead of responsibility and performance, and we are all determined to destroy this system under all conditions."