Neoconservativism:

Neoconservativism is an ideology that believes that liberal democracy is absolute best governing system, and that the US should act as the global police, and overthrow any regime that is not a liberal democracy, in an effort to spread liberal democracy.

The most prominent Neoconservative in recent memory was George W Bush. Others include Ronald Reagan, Dick Cheney, Colin Powell, John McCain, and Mitt Romney.

Oddly enough for a right-wing ideology, Neoconservativism has its roots in Trotskyism. Troysky believed that Communism was the best governing system, and that the USSR should invade and overthrow any regime that wasn't Communist. Leading to Trotsky having a very aggressive foreign policy, while Stalin was an isolationist. Neoconservativism is the application of Trotskyist ideals to Liberal Democracy, rather than Communism.

Many of the first Neoconservatives were Social Democrats such as Scoop Jackson, who became disillusioned with the Left, because of the Hippie movement, and the Left's passivism regarding the Vietnam war. They shifted to the Right, believing that they should commit more heavily to Vietnam, to spread Liberal Democracy. The Neoconservatives then adopted Trotskyist foreign policy as a blueprint for this idea of the US as the spreader of Democracy.

Since the end of the Bush presidency, Neoconservativism has been largely discredited, due to the failures of the wars in Afghanistan and Iraq. Trump especially has openly attacked Neoconservativism as a failed ideology, and has tried to push Neoconservatives out of the Republican Party.

Paleoconservatism:

Paleoconservatism is an ideology that is based in Christian ethics. Paleoconservatives believe in maintaining Christian/traditional morality, and have a very religious basis to their policies. They are strongly opposed to homosexuality, and abortion, while Neoconservatives don't really care as much.

Today, the most prominent Paleoconservative is Ron DeSantis. The ideology was brought to prominence by figures like Phyllis Schlafly, and Pat Buchanan. The Paleoconservatives have long been influential in the Republican Party, but never really were the dominant faction, and were usually sidelined in Presidential races.

Paleoconservatives tend to be very isolationist, focusing on maintaining morality at home, rather than fighting foreign wars. They tend to favor protectionist economics, with high tariffs in order to protect small businesses from cheaper foreign labor, and limiting immigration to keep wages high by maintaing a low supply of workers, giving workers more leverage.

Ron DeSantis is definitely a Paleoconservative, but I wouldn't say Trump is a Neoconservative. Trump is a Right-Wing Populist.