Hidden within this 46-word thicket is the strange idea that liberals are at war with the party’s leadership and seeking to oust its long-serving incumbents — who are themselves, of course, liberals.

It’s not just the Times. Here’s a garbled claim about a year ago from this newspaper: “The Democratic Party’s left-wing insurgency found its limits Tuesday night, with voters favoring establishment candidates over more liberal challengers in almost every closely watched race across several states.” Yet the victors that night in 2018 were actually the more liberal candidates; the defeated challengers who had been seeking to replicate the feat of current Rep. Alexandria Ocasio-Cortez (D-N.Y.) just weeks earlier were not so much liberal as radical or leftist.

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Scads of examples like these are littered throughout the press. For several years now, reporters and pundits have been incorrectly applying the word “liberal” when they mean leftist. This turnabout is ironic. After all, in the 1970s and 1980s, conservatives cynically misrepresented liberalism as an extremist philosophy — basically, a synonym for radicalism. Spiro Agnew, vice president under Richard M. Nixon, briefly popularized the ungainly term “radiclibs.” And although Nixon and Agnew are gone, journalists, it seems, continue to unwittingly carry on their work by blurring the distinction in ways that matter for Democratic politics.

Liberalism has been the governing philosophy of the Democratic Party since Franklin D. Roosevelt, if not Woodrow Wilson: a doctrine of liberty, equality, justice and individual rights that relies, in the modern age, on a strong federal government for enforcement. The party has remained ideologically diverse, ranging from moderates or conservatives — Joe Manchin III (D-W.Va.), for instance, or Rep. Conor Lamb (D-Pa.) — to leftists or radicals, best exemplified today by Sen. Bernie Sanders (I-Vt.) or Ocasio-Cortez and her “Squad.”

Most prominent Democrats, however, including established veterans like former vice president Joe Biden, Pelosi (Calif.), Barack Obama and Hillary Clinton, are liberal.

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So why has liberal come to mean “radical” in seemingly popular usage? In recent years, what was once a left-wing fringe of the Democratic Party has grown significantly. Instead of describing these newcomers and insurgents as “further to the left” than mainstream liberals, reporters succumb to a convenient shorthand, under which those politicians are deemed “more liberal” than the liberals. To clear up the muddle, true liberals like Obama, Biden and Pelosi are recast as “moderates.” And how to distinguish Obama, Biden or Pelosi from genuine moderates like Manchin and Lamb is not explained.

The muddying of the word “liberalism” mirrors, in some ways, what happened to “conservative.” As the Republican Party moved rightward, its most extreme members — whose politics were quite radical and once properly labeled “reactionary”— often were confusingly described as “more conservative” than their cohorts.

Conservatives such as John McCain and John R. Kasich got labeled as “moderates,” while true moderates like Arlen Specter and Jim Jeffords quit the party.

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This reshuffling of terms is problematic, because both conservatism and liberalism are sets of ideas, not simply labels to conveniently identify one half of the political spectrum (itself an imperfect metaphor). Moving left doesn’t necessarily make one “more liberal.” At a certain point, the traveler leaves the province of liberalism for one that is more correctly identified as socialism, radicalism or leftism.

These ideologies or persuasions overlap with liberalism in certain ways, but they stand opposed to it in others. After all, Vladimir Lenin wasn’t “more liberal” than Wilson, and Joseph Stalin wasn’t “more liberal” than Franklin D. Roosevelt. Although their philosophies were “left,” they contained profoundly illiberal ideas. In the days of Wilson and Roosevelt, socialism commanded a comparatively strong following in the United States — party leaders such as Eugene V. Debs and Norman Thomas were household names — and the Democrats pointedly defined themselves against it, as well as against the right, even as any number of policies drew support from liberals and socialists alike.

Needless to say, not every politician or person fits neatly into one category or the other. The labels represent tendencies, not fixed identities.

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Still, some of the biggest conflicts within the ranks of Democratic voters today — and to a lesser degree, among elected officials — turn on the question of adherence to liberal ideas. Some of these conflicts are much more consequential than the hairsplitting debates that are likely to dominate tonight’s primary debate over, say, the minutiae of different health-care or environmental plans.

Perhaps the most salient difference between liberalism and leftism is the former’s commitment to a regulated market economy, as opposed to a command economy. Liberals like Biden or Sen. Elizabeth Warren (Mass.) differ from conservatives in favoring strict rules to make sure the pursuit of profit doesn’t come at the expense of labor rights, consumer rights, the environment or fair competition.

They also reject the vision of leftists like Sanders by seeing a vital role for private business in generating wealth, economic opportunity and innovation. The battle last year over bringing Amazon’s headquarters to Queens pitted liberal arguments from New York Gov. Andrew M. Cuomo and Mayor Bill de Blasio against left-wing ones from the likes of Ocasio-Cortez. (Amazon founder and chief executive Jeff Bezos owns The Washington Post.)

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Differences between liberalism and radicalism also surface in our ceaseless debates over free speech on campus, online and elsewhere. Seeing equal rights as the cornerstone of a just society, liberals insist speakers should not be silenced for expressing unpopular or offensive views.

A growing faction on the far left, however, mirroring elements of the religious right, favors denying free-speech rights to those who hold ideas it believes crosses inviolable lines — leading to incidents like the assaults on political scientist Charles Murray at Middlebury College or conservative journalist Andy Ngo in Portland, Ore. (The appropriateness of preemptive violence can also be a dividing line between liberalism and radicalism.)

In foreign policy, too, rifts in the party these days mostly arise not between centrist and liberal ideas, but between liberal and leftist ones. Liberalism has no truck with authoritarian regimes of the left or those that claim a revolutionary mantle, whether Nicolás Maduro’s Venezuela, the Castro family’s Cuba, Bashar al-Assad’s Syria, Hamas and Hezbollah, or even Vladimir Putin’s Russia. (Whether the former Communist KGB operative deserves to be labeled left- or right-wing is a complex issue.) Some left-wing politicians, journalists and academics, by contrast, express admiration for these figures and minimize their crimes, in part because they align themselves against the United States and its alleged imperialist predations.

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On a host of other issues as well, a liberal-vs.-leftist division is emerging: free trade, U.S. leadership in the world, immigration, identity politics. Meanwhile, centrists are virtually absent from the debate. Among the two dozen Democratic candidates running for president this year, only one or two can justifiably be called centrist. The days of a candidate like Ernest F. Hollings (in 1984) or Joseph I. Lieberman (in 2004) mounting a credible bid for the party’s nomination are gone.

If the rifts are real, why do the labels matter?

Because they shape our perceptions of the political landscape. Terms like “centrist” and “moderate” are nowadays flung as terms of insult or abuse, badges of weakness or tepidness. In 2016, Sanders, joined by the media, inflicted lasting damage on Hillary Clinton’s reputation by casting her in this light, as a betrayer of liberal values: a “hawk,” a shill for big business, even a racist. Her approval ratings, which stood at 55 percent among his supporters when his attacks began in late 2015, plummeted to below 40 percent by the next spring, when she had sewn up the nomination.

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But Clinton was a liberal, not a centrist, as are Pelosi, Biden and most of the other Democratic presidential contenders. Denying them the liberal label and reserving it for Warren and Sanders skews voters’ understanding of their politics.