“Thanks again for making this movement possible,” said another recent campaign email, this one from Senator Elizabeth Warren of Massachusetts.

[Sign up for our politics newsletter and join the conversation around the 2020 presidential race.]

Democratic candidates are desperate to brand themselves as true champions of the people, free of corporate interests and deference to big money. But while only three major candidates — Ms. Warren, Beto O’Rourke of Texas and Senator Bernie Sanders of Vermont — have, to this point, sustained their campaigns through small-dollar donations, it has not stopped others from characterizing their bids as true “grass-roots movements.”

This includes Senator Kirsten Gillibrand, even as she gathered donations at the home of an investment banking mogul, and Senators Kamala Harris and Cory Booker, who have feasted on California’s elite donor circuit.

The language shift also reflects a party that is seeking to appease its activist base, which has been emboldened since President Trump’s victory in 2016.