NOT A RHETORICAL QUESTION!
Being not American, I just earned that there is this extreme-right party called "Constitution Party". What is exactly the difference between them and Republicans? What is the difference between "paleo" and "neoconservativism" (other than meaning ancient and new, of course, please don't answer that, I know basic Ancient Greek too.)
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This isn't a party.
This is a party that several Republican politicians have threatened to create and secede to if Trump is able to secure the Republican nomination at the national convention.
Neoconservatism is a political ideology that espouses a return to "traditional" policies regarding trade and capitalism, and an aggressive, interventionalist foreign policy. Neoconservatives were a minority in the republican party for several decades, as their extreme right-wing policies had no chance to fly with voters. However, since the 1980s, they have been steadily growing in the House and Senate and now the majority of Republican leadership subscribes to neoconservative views, if they don't consider themselves neocons outright.
I've never heard the term "paleoconservative" coined in any fashion. It's likely a derogatory term coined to draw attention to the fact that most neoconservative policies are regressive, out of date and out of touch with modern views.