Even as Senator Bernie Sanders of Vermont has fired up the American left over the past decade, his speeches have the flavor of a sociology lesson. He rarely makes himself the main character.

Which is why it is striking how differently the young leader often seen as his successor, Representative Alexandria Ocasio-Cortez of New York, approaches politics.

As she kicked off a Western tour with Mr. Sanders on Thursday in North Las Vegas, Nev., she introduced herself by name — which he never does — and used her experience waitressing to explain her politics to a crowd of several thousand people.

“I don’t believe in health care, labor and human dignity because I’m a Marxist — I believe it because I was a waitress,” she said. “Because I worked double shifts to keep the lights on and because on my worst day, I know what it feels like to feel left behind. And I know that we don’t have to live like this.”

Mr. Sanders, by contrast, delivered a version of the same speech he has given since before Ms. Ocasio-Cortez was born, railing against corporate greed. “Eat the rich,” someone yelled.