Democracy is under threat in its historic heartlands, Europe and the US. Right-wing strongmen such as Viktor Orbán in Hungary, Recep Tayyip Erdoğan in Turkey and Jarosław Kaczyński in Poland are curtailing civil liberties, removing the independence of the judiciary and muzzling the press. In other countries, antidemocratic parties are riding high on a wave of public hostility to immigrants. And then there is Donald Trump, who, as we have seen during his recent European tour, is potentially a far more disruptive and dangerous figure than any of these, because as US president he wields an influence that is global in scale.

There can be little doubt about Trump’s hostility to democratic institutions or his contempt for democratic standards of public discourse. He defames his critics as liars, calls for the suppression of newspapers that expose his falsehoods, attacks judges who rule against him, urges the wider use of firearms in society, expresses sympathy for white supremacist demonstrators, withdraws demonstratively from international alliances and organisations, and suggests that becoming president for life might not be a bad idea.

For some concerned observers, it’s all too reminiscent of the 1930s, when democracies were destroyed all over Europe and dictators plunged the world into the bloodiest war in history. But are we really witnessing the revival of fascism? Madeleine Albright, US secretary of state under Bill Clinton, certainly thinks so. Economic and social crisis, weak democratic parties and compliant conservatives all helped bring fascism to power then, and look very much as if they are doing so again today. “If we think of fascism as a wound from the past that had almost healed, putting Trump in the White House was like ripping off the bandage and picking at the scab,” she writes.

Trump is one of a kind with such tinpot dictators as Maduro, Erdoğan, Putin, Orbán and Kim Jong-un Madeleine Albright

Trump is “the first antidemocratic president in US history”. He “flaunts his disdain for democratic institutions, the ideals of equality and social justice, civil discourse, civic virtues, and America itself”. He is one of a kind with such tinpot dictators as “Maduro, Erdoğan, Putin, Orbán, Duterte and – the sole example among them of a true fascist – Kim Jong-un”.

At this point, if it hasn’t been clear earlier in the book, it becomes apparent that Albright doesn’t really know what fascism is. Lumping together post-Stalinist dictators such as Kim Jong-un and Nicolás Maduro with rightwing nationalists such as Orbán and Vladimir Putin is not much help in understanding either the forces that brought them to power or the policies they are implementing. Albright seems to identify fascism simply with a hostility to democracy and a propensity to lie. There’s a vast literature on its history and politics, but this might as well not exist as far as she is concerned.

For the Nazis, for example, she relies mainly on Alan Bullock’s biography of Hitler, published in 1952. Her account of fascism’s history is shot through with errors, great and small. The German inflation of 1923 did not destroy the middle classes. German surplus capital did not all go to pay reparations, which in any case were suspended well before the Nazis came to power. The Nazi flag was designed in the colours not of the German republic but of the German empire. Oswald Mosley did not have a toothbrush moustache. And so on.

Why does any of this matter? If we fail to identify how the threat to democracy operates or why it succeeds in some places and not in others, we won’t be able to offer any effective opposition to it. Fascism, as Albright correctly notes, used mass violence against its opponents to bludgeon them into submission as a means of overcoming them. Today’s threat to democracy, surely, is more insidious, involving, as a start, a populist appeal to voters that produces the kind of overwhelming electoral dominance that Hitler, who never secured more than 37.4% of the vote in a free national election, failed to achieve. That is why he deployed hundreds of thousands of stormtroopers, following the example of Mussolini’s squadristi, to turn democratic success into dictatorial power. For today’s enemies of democracy, it is the coercive institutions of the state that play the key role, not private armies of thugs.

True, racism was at the heart of German nazism and, though in a different way, Italian fascism, but it’s not the core ideology of late-communist regimes such as those in North Korea, Cuba or Venezuela. In Europe and the US at the moment, to paraphrase the famous declaration of a democratic politician in the Weimar republic, “the enemy stands on the right”, not on the left.

In The Road to Unfreedom, the historian Timothy Snyder also sees Trump as engaged in “a turn away from democracy and the rule of law”. Trump said he would reject the presidential election as rigged if he did not win, hinted that Hillary Clinton might suffer violence if she pushed for stricter gun controls, and spread “internet memes from fascists”. He is not a populist but a “sadopopulist”, winning support from deprived masses only to implement policies, notably in healthcare and tax reform, that were designed to hurt them. Of course, the hallmark of populists is that their rabble-rousing rhetoric does not really hold out the promise of improving opportunities for the masses, as Snyder supposes: its promises, such as halting immigration, or reviving obsolete industries, are all snake-oil medicines.

Snyder, too, seems to equate hostility to democracy with fascism. He is as vague and confused about its history as Albright is. But where the former secretary of state provides an oversimple analysis of the travails of democracy, the Yale professor offers an overacademic one, calling as witnesses a procession of obscure Russian thinkers, above all Ivan Ilyin, whom he regards as fascist. But many of these were not really fascist at all by any commonly accepted definition: Ilyin, for example, was conservative, religious and monarchist in his views, while fascism was radical and revolutionary, anti-religious and highly critical of the traditional institution of monarchy. Ilyin, moreover, was strongly opposed to German nazism. What united all these thinkers was their ultra-nationalism, which is why they are being taken up by Putin; but ultra-nationalism is not the same as fascism, for all the things they have in common.

Britain and France had no modern history as nation-states. The European powers had never been nation-states Timothy Snyder

The effectiveness of Snyder’s thoughts on the “road to unfreedom” isn’t helped by the strangely declamatory, often obscure style in which they are expressed. One dubious generalisation follows another, as the author never troubles to support any of them with serious evidence. For instance: “Britain and France had no modern history as nation-states. The European powers had never been nation-states.” Does Snyder really think that the possession of an overseas empire negated the claim of the imperial power to be a nation-state? Or: “The meaning of each election is the promise of the next one.” Most people think the meaning of an election is defined by the policies of the parties that contest it. And so on.

Obsessed with the theory of Russian manipulation behind all the political surprises of recent history, from the Brexit vote to the election of Trump, he has little to say about the driving forces behind them, forces that are vital to understand if democracy is to be saved. And by packaging all of this in the endlessly repeated concepts of “the politics of eternity” and “the politics of inevitability”, he virtually guarantees that he will lose the attention of his readers. The current threats to democracy cry out for reasoned and powerfully expressed analysis, but regrettably, neither of these books comes anywhere near to offering it.

• Fascism: A Warning by Madeleine Albright (William Collins, £16.99). To order a copy for £14.44, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.

• The Road to Unfreedom: Russia, Europe, America by Timothy Snyder (Bodley Head, £25). To order a copy for £21.25, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.