This is a very good question. I think it is quite common for people to link the two movements but they are, in fact, quite different. Their common goals may have been similar, at least in regard to practical policy, but their origins and worldview were dissimilar.
For example, Tom Watson of Georgia–Dr. Woods references C. Vann Woodward’s biography–was linked to Alexander H. Stephens and Robert Toombs, and they, in turn, represented the old Jeffersonian critique of Hamiltonianism. At its core, Populism was no different. The Midwestern bunch readily dropped their disdain for central government, realizing they cut a raw deal with the New England Republicans in 1854 when the Party was formed. The state capitalists got the gold mine, they got the shaft, and since the powers of government had already been used against them, why not turn it on its head and use those same powers to “regulate” the “free market,” which of course was heavily subsidized, at least in regard to railroads.
In short, American populism is the Jeffersonian agrarian critique of economic reconstruction. Progressivism, which its disdain for organized religion, origins in European Marxist theory, and focus on social “reform” no way matched the intellectual underpinnings of American populism. William Jennings Bryan used a “cross of gold” as a reference that every God-fearing farmer would understand in his famous 1896 Democratic Convention speech. And remember Bryan was the “prosecuting attorney” in the Scopes “trial.” Clarence Darrow was the progressive “defense attorney.”
I touch on this topic in the chapter on the Lindberghs in my “Forgotten Conservatives in American History.”