I think they are known as the resistance because the New Republic had demilitarised themselves after they defeated the empire, so the resistance is basically just the Rebel alliance v2, just resisting the New Order I suppose.

Basically New Republic is the democracy state/ Senate, pretty much how it was in the new trilogy how they commanded the clone army, just they have no clones or any army anymore so they can't do anything to defend themselves.
The resistance is independent to the New Republic as it is commanded by Leia so if it wasn't for them there would be nobody to stop the New Order taking over the New Republic.
And then the New Order is the Empire v2, just more like how the Droid army was in the sense that they were not part of the Republic but wanted to take control. (Whereas the original Empire had complete control over the republic government)