It’s a mistake to label the fight in the Democratic party as one between “moderates” and “progressives.”

“I am not a member of any organized political party,” the early 20th-century comedian Will Rogers once said. “I am a Democrat.” Nearly a century later this quip remains apt. This fall, when the party looks likely to retake control of the House of Representatives and has an outside shot to win the Senate, Democrats seem to be delighting in fighting one another.

To hear the pundits tell it, the cleavage runs deep between the party’s “progressive” and “moderate” factions. But this understanding, and the terminology that goes with it, is wrong. In truth, few moderate Democrats remain in national office. The split is now a different one: between liberals and leftists. Understanding this distinction matters as voters assess the candidates vying to lead the party during — and after — the Trump presidency.

This confusion occurs because for two generations, party fault lines did in fact run between liberals and centrists.

Starting in the turmoil of the late 1960s, Democrats — once the nation’s majority party — found themselves on the defensive. From 1968 to 1988, they lost every presidential race but one (Jimmy Carter’s razor-thin post-Watergate win in 1976), several of them in landslides, and lost ground in state and local contests as well. The party’s support for civil rights had caused the once-Democratic South to gravitate slowly but inexorably toward Republicans, while its leftward shift on foreign policy, crime, welfare and other cultural issues alienated working-class whites elsewhere — Nixon’s “Silent Majority” and the vaunted “Reagan Democrats.”

Many concluded a more pragmatic politics was needed to regain power. In 1972, after the party nominated the ultraleft Sen. George McGovern of South Dakota, a group called the Coalition for a Democratic Majority tried to unite Democratic moderates but made little headway. Then in 1985, the Democratic Leadership Council emerged as a far more effective successor groups.

The Democratic primaries of 1984 exposed the split, with the old-line liberal Walter Mondale facing off against youthful Sen. Gary Hart of Colorado and his self-proclaimed “new ideas.” (“Where’s the beef?” Mondale famously asked.) The 1988 field contained both unreconstructed New Dealers like Paul Simon of Illinois and more moderate DLC figures like Bruce Babbitt of Arizona and Al Gore of Tennessee. ...