At its heart, modern conservatism is defined by its antipathy to liberalism. Whereas intellectually, it is differentiated by its four heads: (1) traditionalism; (2) neoconservatism; (3) libertarianism, and (4) the religious right. You can read a summary of Ceaser's argument below:

https://lawliberty.org/four-heads-and-one-heart/

I, however, have a less charitable take than Ceaser. Modern conservatism, IMO, is increasingly authoritarian. Conservatives are more than willing to compromise on their so-called intellectual principles, in order to rally behind an authoritarian strong man: especially during moments of perceived crisis. According to Nazi jurist Carl Schmitt, neo-conservatism is reducible to the distinction between friend and enemy. And this distinction is far from logically consistent; it is whatever distinction authoritarian leaders are willing to make in order to maintain the legitimacy of their rule -- especially when that rule undermines the existing rule of law and the ability of the legislature to check executive power.

https://aeon.co/essays/carl-schmitts-legal-theory-legitimises-the-rule-of-the-strongman