The New Right, to me, are the rabid anti-gay, anti-Islam, anti-marijuana, anti-social-liberalism brigade.
Neocons are just neoliberals with a penchant for military interventionism and aggressive foreign policy. Born from 9/11 and Chinese monetary hijinks.
The "New Right" is just what everyone calls the "alt-right" then. Funny enough, Mr. Alt-Right himself, Richard Spencer endorsed Biden!
If we're thinking the new Trumpian right: it's more anti-immigration, anti-terrorism (but also anti-war), anti-taxes, anti-regulation. LGBT isn't really something that's a priority. And I'd say at least are classic liberal and but socially conservative.
But the Neocon definition is pretty spot-on.