The answer to this is that in modern political science discourse, "populism" does not simply stand for the Cambridge Dictionary definition ("the espousal of policies that achieve popular support", as another answer here suggests; in fact, one of the leading scholars on populism has criticized the Cambridge Dictionary in an article in the Guardian.) A better summary/definition of populism, according to one paper is that:
there is wide consensus in the literature that populism as an ideology
includes the following elements: (1) an assumption of a central antagonistic
relationship between ‘the people’ and ‘the elite’; (2) an attempt to give power
back to the people and restore popular sovereignty; and (3) a perception of
the people as a homogeneous unity (Canovan 1999; Mudde 2004; Mény and
Surel 2002). In addition, populism often involves announcing a serious crisis,
claiming a central position for the leader who embodies the will of the people,
and conducting adversarial politics; i.e., a strategy of polarization. Besides this,
however, populism is ‘empty’ as a substance. It is, using the concept developed
by Michael Freeden, a ‘thin-centred’ ideology, which can be attached willynilly
to any left- or right-wing political ideas (Mudde and Kaltwasser 2014).
Or in more exemplified detail, focusing on the 3rd aspect:
Contemporary populism can be characterized by its rejection
of social and cultural pluralism and its emphasis on an imagined
homogenous people. An often nostalgically conjured
“we” should distinguish itself from the “they,” the “other.”
I follow in this regard the definition of Jan-Werner Müller, a
German political scientist at Princeton University:
In addition to being anti-elitist, populists are
anti-pluralist. They claim that they and they
alone represent the people. All other political
competitors are essentially illegitimate, and anyone
who does not support them is not properly
part of the people.When in opposition, populists
will necessarily insist that elites are immoral,
whereas the people are a moral, homogeneous
entity whose will cannot err.
Examples of such claims to represent the true people excluding
all those who do not concur abound among contemporary
populisms. In Austria, Jörg Haider and Heinz-Christian
Strache, leaders of the right-wing populist party Freiheitliche
Partei (FPÖ), expressed the apparent unity of the will of the
people with the slogan “HE says what YOU think.” Hugo Chávez, the former president of Venezuela, addressed his
“people” by claiming to be “a little of all of you.” During
the election campaign his personification of all the people
was expressed by slogans like “Chávez is the people!” or
“Chávez we are millions, you are also Chávez!” The Turkish
president Recep Tayyip Erdogan gave an example of the
populist temptation to exclude all those who do not agree
with him by asking his numerous domestic critics: “We are
the people. Who are you?” From a populist perspective,
the ordinary people are juxtaposed to manipulative elites.
Finally, we also see this monopolization of the people in
United States president Donald Trump's inaugural address in
2017, claiming that on this day “we are not merely transferring
power from one administration to another, or from one party
to another—but we are transferring power from Washington,
D.C. and giving it back to you, the American people.” It did
not trouble his identification with people at all that his rival
candidate Hillary Clinton gained nearly three million more of
the popular vote than he did.
Similarly also Alexander Gauland, the front-runner of the
German far-right populist party, Alternative für Deutschland
(AfD), explained in a television debate after the national elections
in fall 2017 that now his party will “take back our country
and our people.”
There also those [political scientists] who (more skeptically) argue that the term is of limited utility in describing anything, as Stanley (2008) did:
The concept of populism has in recent years inspired much debate and much confusion. It has been described variously as a pathology, a style, a syndrome and a doctrine. Others have raised doubts as to whether the term has any analytical utility, concluding that it is simply too vague to tell us anything meaningful about politics. Drawing on recent developments in the theoretical literature, it is argued that populism should be regarded as a ‘thin’ ideology which, although of limited analytical use on its own terms, nevertheless conveys a distinct set of ideas about the political which interact with the established ideational traditions of full ideologies.
But the same paper also goes toward answering your question...
The stigma attached to populism is itself evidence that
populism exists as a distinct pattern of ideas, even if it has generally been regarded
as something to be feared and discredited. Critics of populism typically charge
their targets with demagogic practices: for playing on popular emotions, making
irresponsible and unrealistic promises to the masses, and stoking an atmosphere of
enmity and distrust towards political elites. The nature of this criticism has
contributed to populism’s being associated with demagogy to the extent that the
two concepts are frequently conflated.
I.e., if you call someone a populist it's more like calling them a demagogue rather than a democrat. Echoing one of the answers here though...
a number of populists have responded to
being labelled as such through the rhetorical flourish of accepting an epithet
conferred by ‘the enemy’ whilst simultaneously rejecting its negative
connotations. The declaration of one prominent contemporary populist illustrates
this move well:
Populism precisely is taking into account the people’s opinion. Have people the right, in a
democracy, to hold an opinion? If that is the case, then yes, I am a populist.
(The paper is quoting Jean-Marie Le Pen.)
Nevertheless this paper also acknowledges a slightly more substantial notion of populism than merely equating it with demagogy, even when used pejoratively:
whilst the critics’ purpose may be
to delegitimise populists, in pointing out the characteristic manifestations of
populist demagoguery they acknowledge the existence of a distinct pattern of
thought-practices: the division of the political into two opposed and antagonistic
groups, the assumption of an essential harmony of interests among ‘the people’,
and the assertion of the normative and moral legitimacy of this ‘people’s will’ as
the basis for decision-making. [...]
The concept of ‘the people’ is characterised by both ‘rhetorical usefulness and
. . . conceptual obscurity’. In articulating a structure in which the political is
divided into ‘the people’ and ‘the elite’ populists exploit this rhetorical usefulness
whilst side-stepping the question of complexity. [...] The populist subscribes to the Schmittean doctrine that ‘[t]he specific political
distinction to which political actions and motives can be reduced is that between
friend and enemy’. The relationship that obtains between these two groups is of a
more intense nature than simple ‘difference’, it is a relationship of profound
otherness and, in the extreme case, conflict.
The paper gives as illustration quotes the discourse of some fairly obscure Polish party (the Self-Defense Party), which I'm omitting here because a decade later one can find much more prominent examples of such discourse.
In general, in the West today "populism" is used to tag identitarian and illiberal movements and less often "economic populism".
Also, I think the accepted answer is horribly blurring the lines between populism and democracy, but such a confusion is perhaps understandable given the flexible meaning assigned to both terms by various sources... Granted, there is a tangent here that the "tyranny of the majority" is related to (identitarian) illiberalism.
Stanley's paper notes that populism isn't simply an appeal to majoritarianism:
The concept of majoritarianism has moved close to the core of populism,
particularly in the era of mass franchise where attempts to separate the legitimate,
propertied people from the ‘idle and indigent rabble’ are clearly anachronistic.
Populists are often to be found advocating the use of methods of direct democracy
on the assumption that these instruments allow the majority voice to have an
impact on decision-making and agenda-setting. However, support for direct
democracy is not an essential attribute of populism. The importance of
majoritarianism for populism is that it helps to reinforce the authenticity of the will of the people. The greater a majority in favour of a particular policy or moral
value, the more credibly it can be said to reflect the popular will. Ultimately,
though, what is most important is to appeal to the idea of an authentic people.
The invocation of authenticity and ordinariness is a key aspect of populism’s
appeal to the people, as it allows populists to lay claim to genuine representativeness.
In other words, one can be a populist without being terribly democratic. For example:
The manner in which these identifications occur will depend on the particular
context in which a populist discourse is articulated: the populist has access to a
wide repertoire of possible antitheses but not all will be relevant and credible in the
circumstances. Where ethnic origins are (or can be presented as) salient to the
context of elite/popular antagonism, the positive valorisation of the people can be
expressed in terms of the superior virtues of a particular ethnicity, and the elite
denigrated in kind as either outsiders or multiculturalist ‘ethnic traitors’.
The plasticity of the concept of ‘the people’ assists the individual populist, for
whom it can expand or contract to suit the chosen criteria of inclusion or exclusion.
However, the openness of this concept has hampered the development of populism
as an ideology in its own right. In order to engage with politics in the concrete, the
abstractions of core concepts must be translatable into those peripheral concepts
which link ideology to a particular context. The particular vagueness of the people
makes it very difficult to do this, impeding the development of an intellectual
tradition possessing a fuller range of responses to political questions.
This is why "populism" by itself seldom (if ever) describes a political movement well enough. In general one needs to assert some "essential" characteristics of "the people", e.g. ethnic or economic, to get any further down the ideological road, hence descriptors like "right-wing populism", or better "identitarian populism" for some contemporary movements.
But even on this "thin level" definition of populism (that does not get into pinning down the characteristics of "the people"), there are basically two ways to be critical of (or antithetical to) populism: elitism and pluralism.
we argue that one aspect of this definition that has not been sufficiently taken into account in the scholarly debate is that populism has two direct opposites: elitism and pluralism. Those who adhere to elitism share the Manichean distinction between ‘the people’ and ‘the elite’, but think that the former is a dangerous and unwise mob, while the latter is seen as an intellectually and morally superior group of actors, who should be in charge of the government – technocrats are a key example of this.
In contrast to populism and elitism, pluralism is based on the very idea that society is composed of different individuals and groups. Therefore, pluralists not only avoid moral and Manichean distinctions, but also believe that democratic politics is about taking into account diversity and reaching agreements between different positions. As Paulina Ochoa Espejo has rightly noted, those who adhere to pluralism are commonly inclined to think of popular sovereignty as a dynamic and open-ended process rather than a fixed and unified will of the people.