I think I will now slightly modify what I said before, that populism is any political movement that flatters the common people for their superior virtue and/or wisdom and especially for their authenticity. I reached this conclusion because of another political movement, predating the American Populist Party that is sometimes translated as Populist -- the Russian Narodniks, narod meaning "the people" in the populist sense.
The two movements were similar in that both praised and flattered the common tillers of the soil for their superior virtue and authenticity. Otherwise they were not alike. Russian Narodnichestvo was a movement of middle class urban intellectuals trying to awaken a politically detached and passive peasantry into assuming the revolutionary role that the Narodniks had envisioned for them. It never gained any significant following among the Russian peasants, who continued to be politically passive and not the least revolutionary. American Populism was a grassroots, bottom-up movement among politically active and engaged farmers, accustomed to participating in democratic politics and angry that their voices were not being heard and their concerns addressed. It was not a revolutionary movement, but one that sought to achieve its goals within the existing electoral framework.
Populism from above versus populism from below
So I would say that a populist movement is not merely one that praises the common people for their superior virtue and authenticity, but one that has a significant popular following. "Significant popular following" need not mean the whole people, or the whole lower classes. It need not even mean a majority of either group; a significant minority is sufficient. But it has to have a large enough following to be an actual popular mass movement and not merely a leadership vainly looking for followers.
This raises at least one distinction between forms of populism. A populist movement can be an emanation from below that only later finds its leadership, or inspiration from above, that finds a receptive audience. A populist movement that springs from below could be called organic populism or grass roots populism. A populism initiated above but inspiring a strong following might be called top-down populism, leader-oriented populism or (by its enemies) demagogic populism. To be truly effective, a populist movement must have both effective leadership (including access to the corridors of power) and strong popular support. Leadership without followers will go nowhere, like the Narodniks, while a grassroots movement without leadership will lack direction and quickly burn out.*
Revolutionary versus electoral populism
Comparing the Narodniks to the Populists also raises that least the suggestion that a populist movement must arise from a politically active and engaged public, accustomed to participating in democratic politics and angry that their voices were not being heard or their concerns addressed. If this is true, populist movements can only take place in the context of democratic politics, by people who feel left out and regard inclusion as their right.** I don't agree though, that populism is necessarily a movement that (a) seeks power through electoral democracy rather than revolution and (b) undermines and subverts democracy upon achieving power. For instant, the fascist movements are generally considered populist, but they fully intended the revolutionary overthrow of democratic government and merely treated electoral politics as a means to this end. On the other hand, there is no reason to believe that every movement in democratic politics that flatters the common people and appeals to people who feel left out necessarily endangers democratic pluralism. One can imagine a President Williams Jennings Bryan continuing to respect the democratic process. So too, the Brexit has been called a populist upsurge, yet it took place under the Conservatives, whose commitment to democratic pluralism is not in doubt. And the UK Independence Party has condemned many of the excesses of the French National Front.
That raises another distinction between forms of populism. There are populist movement that seek to overthrow democratic politics altogether, even if they may they compete in elections as a temporary expedient. This might be called revolutionary populism. (Fascism is a form of revolutionary populism). And there are populist movements that do not seek to overturn elective government but only to advance their interests within an electoral framework. These may be called electoral populists.
Selective versus pluralistic populism
Just because a populist movement does not intend to overthrow elective government does not negate its danger to democracy, however. There are populist movements that do not mean to end electoral politics, but are profoundly subversive of democracy because they read anyone who disagrees with them out of "the people." I will follow Umberto Eco in calling that selective populism. And there is populism that flatters the virtues of the common people, but also recognizes disagreement as legitimate. That might be called pluralist populism. Note, too, that there can be a populist movement among a specific interest or identity group -- anti-elitist posturing, flattering the group for its authenticity and virtue, and building a strong popular following based on the sense that the group has been denied its right of inclusion -- that simply seeks a seat at the table, or a larger share of political power. There is much to criticize in identity or interest group politics, but at least it has the virtue of being able to resist the lure of selective populism or of considering itself a Volkspartei and writing dissenters out of "we, the people" altogether.***
Hope, fear, or resentment
There are other differences as well. Any political movement that seeks to appeal to the common people will appeal to emotions and not be wonky. But which emotions? It can appeal to aspirations and be a hope-based or aspiration-based populism. It can appeal to resentments and be a resentment-based populism. Or it can fear-monger and be a fear-based populism.
Left-wing versus right-wing populism
Populism necessarily proclaims the moral superiority of the common people to oppressive elites. It does not (normally) champion minority identity groups and sometimes treats them as scapegoats. It generally leans left on economic issues and right on social issues. It can be left-wing or right-wing depending on which it emphasizes more, economic or social issues; punching up or kicking down.
So, I would identify populism as a movement within democratic electoral politics that appeals to people who feel shut out or excluded; treats this exclusion as a violation of a democratic rights; flatters their superior virtue, wisdom or authenticity; and has a significant popular following. It often addresses genuine and legitimate grievances. To the extent that it demands a voice for those who have been denied one, it can serve a valuable role. But flattery and resentment (and how can anyone not resent being denied a voice, or having legitimate grievances ignored?) are dangerous. And populist movements tend to be inherently politiphobic, i.e., impatient with the sort of political maneuvering at the top that is inevitable and essential to getting things done. As such, there is probably in inevitable authoritarian streak in populism. But it is not necessarily dominant.
Populist movements can be top-down or bottom-up, although it can be extremely difficult to tell the difference. They can be revolutionary, or respect electoral politics. Populists who respect electoral politics can be selective populists (reading dissenters out of "the people") or pluralistic. Populism can appeal to hope and aspiration, to fear, or to resentment. (Usually some combination). It can be of the right or the left.
So, in the future, when writing about populism, I should pay attention to these distinctions.
So far, the only populist I have encountered so far in my history of failures of democracy has been Pesistratus of Athens.**** Our records on him are a bit sketchy, but he appears to have been a demagogic, revolutionary, aspiration-based, left-wing populist. That is to say, he appears to have organized and inspired a previously passive poor majority that was being left out and resented it. He sought to overthrow the democracy and establish himself as dictator. He appears to have appealed more to people's hopes and aspirations than their fears, and to have punched up rather than kicking down. And, surprisingly enough, he also seems to have been a first-rate ruler. Others in his place have not done so well.
I expect to encounter many more populists, although by no means all failures of democracy have been at their hands. When I do, I will make the attempt to classify them by the categories set forth here.
*The Tea Party is an interesting example. It has both a strong grassroots organization and a strong leadership, but (at least until Trump came along), the leaders and the followers pursued different agendas. The leaders were hardcore libertarians, seeking (ultimately) to roll back the New Deal, while followers were not opposed to government spending in general, but to spending on people seen as unworthy, and to illegal immigration.
**Thus also the populist movements in Classical times, from Pesistratus of Athens (and perhaps Cleon as well) to the Gracchi, Marius, and Caesar in Rome. All competed in the arena of electoral politics, but they had very different ideas about the long-term future of electoral government.
***Although it might be troubled by what could be called selective identity group populism, i.e., the believe that any member of its sub-group is not an "authentic" or "real" member. Thus the anger of many black conservatives at being treated as not "authentically" or "really" black.
****Proof, incidentally, that populism is by no means the only threat to democracy. The threat can come from people who are openly opposed to democracy, favoring oligarchy or dictatorship instead. The only reason populism seems like the greatest threat to democracy today is that open anti-democrats have become so rare.