Some in the media and many political pundits have referred to President Trump as a populist or a fascist or both. These terms are not opposites, but they aren’t comfortable bedfellows. I cringe every time I see Trump referred to as a populist because my vision of populism is the inclusive, broad-based populism of Senators Bernie Sanders and Elizabeth Warren.
A populist is someone who supports the concerns of ordinary, working people, as opposed to the elite, upper class. Populist activism is based on the belief that the common people are being exploited by the privileged elite. The underlying ideology of populists can be left, right, or center. Populist activism becomes likely when mainstream political institutions fail to deliver economic and social well-being for ordinary people.  The direction that populist activism takes depends heavily on the style of the politician who taps into it.
Populism has a long history in the US. There was a Populist Party in the 1890s and William Jennings Bryan ran as the Democratic presidential candidate on a populist platform in 1896, 1900, and 1908. President Theodore Roosevelt and the Republican Party took over the populist banner in the early 1900s. George Wallace’s campaigns of the 1960s and 1970s had populist themes that some labeled reactionary populism due to their racist underpinnings. Ralph Nader in the 1990s and 2000s ran for president using populist themes.
Trump’s campaign and presidency have a populist element in their appeals to the working class. However, their focus on the white working class evokes memories of the reactionary populism of George Wallace. Trump argues that the working class is being hurt by the actions of political elites in Washington, D.C. He also appeals to the working class by asserting that their well-being is being undermined by immigrants. There is a racist element to Trump’s appeals, as he lays the blame for the struggles of the white working class on (largely Latino) immigrants and Blacks. Historically, this type of reactionary populism has been fertile ground for the development of fascism.
Some view Trump’s populism as faux-populism and demagoguery because his appeals to the working class are based only on rhetoric and unrealistic policy proposals. Trump exhibits attributes of a demagogue, such as exploiting the prejudices and gullibility of some voters, and stirring up anger and resentment while eschewing reasoned debate. Historically, demagogues often overturn established customs of political conduct, assert the presence of a national crisis, and accuse moderate and thoughtful opponents of weakness or disloyalty to their country. A demagogic populist typically claims legitimacy directly from the people and asserts that he alone will do what the people want. He refuses to acknowledge the legitimacy of opposition and attacks institutions, from the courts to the news media, that don’t support him. Trump has exhibited many of these attributes. 
Personally, when I think of populism, I think of inclusive populism that is committed to including stigmatized groups (e.g., the poor, minorities, immigrants, and women). They are embraced and supported rather than being targeted for blame and as scapegoats. This is the type of populism that Senator Bernie Sanders promoted during the presidential primaries and for which Senator Elizabeth Warren has been advocating. 
Fascism, on the other hand, is an authoritarian and nationalistic approach to governing where the government controls or partners with business and/or labor. Typically, opposition is not tolerated and the government is led by a strong leader who asserts that strong central control is needed to effectively combat economic difficulties and external threats. A principal goal is self-sufficiency and independence through protectionist economic policies. 
Trump’s rhetoric echoes many of the themes of fascism. Perhaps most prominently, he promotes ethnic stereotypes and fear of foreigners, which is typical fascist rhetoric. Asserting concern about national decline is another common element of fascist discourse. Trump’s slogan “Make America great again” fits this theme exactly. Even though the US, by most measures, isn’t in serious decline, he’s able to persuade the white working class that the country is in decline, or at least their position in it is. Poorly-educated white males have experienced economic decline over the last 35 years. The Great Recession of 2008 and the weak recovery from it have left many working people economically worse off. 
Fascists tend to use threats of violence to intimidate opponents and silence critics. They are skilled at getting their followers to believe them even when the narrative they present is at odds with facts; truth becomes subjective.  These are also themes that have been apparent in the Trump campaign and presidency.
Trump’s selections for his Cabinet appear to contradict the populism of his campaign rhetoric. They do, however, fit with fascism’s alignment of business and government. Many of his nominees are from the corporate elite who have played a major role in diverting federal policy from supporting the working class to supporting large corporations. They seem positioned to strengthen the role of the private sector in policy making and undermine the role of the federal government in supporting working people. For example, they have opposed labor unions, workplace regulation, and workers’ rights; they have worked to privatize public education; they have weakened voting and civil rights; they have opposed environmental regulation and action on global warming; and they have supported weakening the social safety net.  
There were and are elements of xenophobic, reactionary populism in Trump’s rhetoric and in some of his (to-date largely symbolic) actions. His style, cabinet nominees, and some of his actions exhibit themes of fascism. Although it’s too early to conclusively decide whether he is more of a populist or a fascist, President Trump has never expressed support for the inclusive populism of Senators Sanders and Warren. On the other hand, he has consistently displayed, and his background seems much more aligned with, some of the core themes of fascism.
 Wikipedia, retrieved 2/18/17, “Populism” (https://en.wikipedia.org/wiki/Populism)
 Wilkinson, F., 2/16/17, “Why Donald Trump really is a populist,” BloombergView https://www.bloomberg.com/view/articles/2017-02-16/why-donald-trump-really-is-a-populist
 The Economist, retrieved 2/18/17, “The Economist explains populism,” http://www.economist.com/blogs/economist-explains/2016/12/economist-explains-18
 Wikipedia, retrieved 2/18/17, “Fascism” (https://en.wikipedia.org/wiki/Fascism)
 Chotiner, I., Feb. 2016, “Is Donald Trump a fascist?” Slate (http://www.slate.com/articles/news_and_politics/interrogation/2016/02/is_donald_trump_a_fascist_an_expert_on_fascism_weighs_in.html)
 Kuttner, R., 12/16/16, “The audacity of hope,” The American Prospect (http://prospect.org/article/audacity-hope)
 Vanden Heuvel, K., 12/20/16, “Sham populism, shameless plutocracy,” The Washington Post
 Bonham, L., & Jennings, G., 2/17/17, “Is Trump’s billionaire cabinet actually a closet full of fascists?” Common Dreams (http://www.commondreams.org/views/2017/02/17/trumps-billionaire-cabinet-actually-closet-full-fascists)