No, “liberal” and “progressive” aren’t synonyms. They have completely different histories—and the differences matter

Sean Wilentz in Democracy Journal:

What’s in a name? Franklin Delano Roosevelt called himself a Christian, a Democrat, and a liberal. He did not call himself a democratic socialist, or any other kind of socialist. He was, in fact, no socialist at all. Nor was he a conservative or a reactionary, although many on the socialist and communist left charged that he was—including the Communist Party USA, which attacked his New Deal for a time (until Moscow’s political line changed) as American “masked fascization.”

The only Americans who considered Franklin Roosevelt a socialist were right-wing Republicans. “The New Deal is now undisguised state socialism,” Senator Simeon D. Fess of Ohio declared in 1934. “Roosevelt is a socialist, not a Democrat,” Congressman Robert Rich of Pennsylvania announced on the House floor a year later. Roosevelt scoffed at such talk, but in 1939 he paused to present a very concise political dictionary of his own. “A radical,” he told the New York Herald Tribune, “is a man with both feet firmly planted—in the air.” A conservative, he continued, “never learned to walk forward”; a reactionary walked backward in his sleep. A liberal, though, used legs and hands “at the behest—at the command—of his head.” The metaphor was poignant coming from him, but it also emphasized his point: In the face of all adversity, he was every inch a liberal.

More here.