Neither is the true conservatism.
Both accept the classical liberalism of the American Revolution, Locke, Jefferson, Adam Smith, etc. as foundational principles. Both stress autonomy and the self beyond that which the traditional conservatism of the West would. Both hide behind freedom as I-do-what-I-want to shirk the question of what is good.
In some ways the Trumpish variety is closer because it stresses community over the self to a greater degree. In other ways the standard Republicanism is closer because it, or at least parts of it, attempts to make some argument about what good is. But neither is really conservative.