Let’s be careful here.
This purported explanation — that the Trump admin is explicitly echoing a slogan coined by the Nazis — has ripped across the web like wildfire. It fits perfectly with the moment and has the ring of truth.
Historians, however, are scrambling to catch up, and the best information at the moment seems to be that while the premise of the slogan does align with Nazi practice, per the widely cited Lidice precedent, the phrase itself was not coined or used by the Nazis in any similar or recognizable form.
There is this ongoing discussion in the “Ask a Historian” Subreddit, which also includes some interesting speculation about how the slogan might even have been expressed in German, were it to have been used. There is also this Substack essay which acknowledges that the slogan reflects Nazi actions, but points to a different potential origin with the Spanish fascists. There is also this analysis which cites the foregoing and several other articles before making the same conclusion: the phrase does strongly embody Nazi ideology, but as yet there’s no identifiable historical source for it.
I’d suggest we refer to it as a “clearly fascist slogan” whose basis mirrors Nazi and other precedents, and which is dangerous for the core idea it conveys — to wit, the inherent “us” vs. “them” premise which allows the world to be divided into those with power and those who are suppressed — without opening ourselves to the accusation of making an almost certainly ahistorical claim. Basically, these guys all come from the same diseased mindset, so it’s not surprising that they wind up independently converging on similar, but not identical, language.