How do they differ, if at all?
Populists on the Right, it's said, got Trump elected. They were very reasonably fed up with loss of jobs, with being replaced by low-wage Mexicans some of whom even lack a permit from the government; and with the smug self-satisfied arbiters of taste and conduct that not only takes their money to fund their colleges but also tells the students what they may and may not say, the First Amendment notwithstanding. They are passionately patriotic and above all, perhaps, they resent being harassed by threats to limit access to guns.
Reasonable grievances, even though neither the voting populists nor their elected champion properly understands all the causes or, therefore, the cures required. There were in 2016 other issues of course, some of which libertarians can applaud: the absurdity of keeping US bases all over the world so as to maintain an American Empire, which heartland populists hardly want.
Last month I came across the current issue of Cato's Letter, in which father and son economists Mario and Alvaro Vargas Llosa discuss populism; and they don't like it. The Cato Institute is one of the best "think tanks" around, and has done fine work since being founded in 1977 with funding from the Koch brothers, administration by Ed Crane, and intellectual leadership from Murray Rothbard. There was however a subsequent split; Rothbard had written his masterly treatise Man, Economy and State but the Kochs didn't want its final third published by Cato; it was too radical for their taste. So he had it published separately as Power and Market, which details how a free market could handle all the functions presently done by government, even including the "caretaker" ones of defense and justice. In other words, it's a scholarly presentation of anarchism; and for whatever reason, the Kochs preferred Cato to promote just Classical Liberalism, which was indeed the economic system that enabled the greatest increase in living standards in the history of mankind. The split was rather acrimonious, with names being tossed around like "Kochtopus" and "Craniacs". That's the background.
The Letter is very well worth reading. The Llosas struggle to define populism and propose that it is a "diseased form of democracy" but there I think they err significantly. On the contrary, it is a more pure form of democracy than what is familiar in each election cycle. In the latter, voters (in the US or anywhere else) are offered a choice between or among candidates who have already satisfied political "experts" that they are fit material for the job. There are for example primary elections within each party, to select their choices. This almost always presents the eventual voter with candidates whose platforms differ only slightly; they are always "mainstream" and rock no boats.
When someone manages to bypass that vetting process (for example because he is wealthy enough to buy publicity and win the primary without support from the Party hierarchy) then, as Trump did, he can offer voters a less orthodox set of proposals; but because he rode roughshod over the vetters, he is scorned as a mere "populist." Even so - whether what the voters want is or is not sensible - he offered what they actually want, and that is very close to pure democracy.
The Llosas remark that democracy brought great prosperity to Venezuela, but that it degraded into populism and that in turn produced communism, led by Chavez; and that ever since, its economy has become a basket case. I was surprised that populism can lead to communism - but they explain that there are Left versons of it as well as Right ones. But how, if at all, did the process there degrade? It seems to me that Venzuelans wanted the goodies that socialists offer, and Chavez provided them. The result, there as everywhere else, has been bankruptcy. This was however the people's choice; it's what they voted for. That's not a diseased form of democracy, it's what democracy always eventually does. In the Venezuelan case, it just did it a lot faster than most.
So Venezuela is a good example of the principle that democracy is two wolves and a lamb, voting on what to have for lunch; and of Madison's insight that "A democracy cannot exist as a permanent form of government. It can only exist until a majority of voters discover that they can vote themselves largess out of the public treasury."
Why in Cato's Letter did the Llosas try to draw a distinction between healthy and diseased democracy? - evidently because they don't want to draw the obvious and necessary conclusion that democracy is just another way of forming a government, and that the problem with Venezuela and every other country lies not in the method of selecting a government, but in the government itself. Their Classical Liberal position is very fine as far as it goes, but it doesn't go far enough.
It's perfectly true (as Madison warned) that democracy is flawed, in that what voters want need not actually be good for them. Venezuela is an excellent case in point. So is the USA; we can go all the way back to when the Constitution was ratified, by a system of endorsement that approximated to a popular vote. See here for what the country would be like if that Charter were faithfully obeyed. And there can be little doubt that here and throughout Europe, voters voted themselves a welfare state, which in every case has seriously impeded economic growth and hindered their standards of life.
But what alternative is possible, if there is to be a government at all? Churchill was surely correct, in saying that democracy is the worst possible form except for all the others. For example if one were to modify a popular vote by some kind of "expert" or scholarly filter, which allowed only those voter wishes that would do little harm in its opinion, then the society would be ruled not by popular will but by those experts; a kind of bureau-cracy.
And so once again we come to the conclusion: there is no rational alternative but to replace government with a free market.