The two back-to-back addresses laid out the competing versions of populism that could come to define the presidential campaign. From the right, there is the strain Mr. Trump brought to maturity in 2016, combining the longstanding grievances of the white working class with a newer, darker angst about immigration and cultural change. And on the left, there is a vastly different populist wave still gaining strength, defined in economic terms by Ms. Warren, Democrat of Massachusetts, and Senator Bernie Sanders of Vermont.

The messages underlined the possibility that the 2020 election could be the first in a generation to be fought without an ally of either party’s centrist establishment on the ballot. While it is by no means certain that Ms. Warren will emerge as the Democratic nominee, two of her party’s top three candidates — Ms. Warren and Mr. Sanders — are trumpeting themes of economic inequality and promises of sweeping political and social reform.

Their version of populism, which Mr. Sanders pioneered but did not bring to fruition when he challenged Hillary Clinton in 2016, is about attacking concentrated wealth and economic power and breaking its influence over government. Ms. Warren and Mr. Sanders, effectively tied for second place in their party’s primary, both describe the country’s political institutions as rotten and vow to make vast changes to the economy.