“His practical program is a program that would be pretty comfortable within the confines of any European country,” said Sheri Berman, a professor of political science at Barnard College. “As far as the policies he’s advocating, those are probably better viewed as social democratic — that’s what they would be in another place in which there are more left options.”

But “because we don’t have a social-democratic party in this country,” Professor Berman said, “the only way to indicate that you want to go further than the Democratic Party — that you are more critical of capitalism than the Democratic Party has been — has been to identify yourself as a democratic socialist.”

And so, even on a question as basic as whether democratic socialism and capitalism can coexist, there is disagreement.

“There are some democratic socialists that would say, ‘Absolutely not,’” Ms. Ocasio-Cortez, who identifies as a democratic socialist, told MSNBC in February. Others — herself included, she said — “would say, ‘I think it’s possible.’”

This complicates the debate

Democratic socialists are not necessarily bothered by the loose definition. There is room for more than one movement on the left, Mr. Sunkara said.

“Socialism means many things,” he said, adding that he tried to avoid policing which self-identified socialists count as real socialists.

But there is little question that the lack of a common definition confuses the political debate.

“Socialist” and “communist” have long been catchall epithets for any proposal that would substantially expand the role of government — including ones, like Social Security and Medicare, that are now popular across the political spectrum. There is a big difference between social-democratic policies and ones that would actually shift control of the means of production, but that distinction is often lost in political discourse.