„Populism is a range of political approaches that deliberately appeal to 'the people', often juxtaposing this group against the "elite".“
There is plenty of left-wing populism, by the way. Jeremy Corbyn, Chavez/Maduro, Yannis Varoufakis, etc.
And no doubt it applies to leftists, absolutely. That's the basis of a lot of right wing views: that the left is simply being populist and doesn't give a shit about actually improving life, but instead staying in power.
Of course, that's about the left's view of the right as well. Hmmmm.
If one had to align them left to right, they would look like:
Sanders -> Clinton -> Bush -> Trump .
> I fail to see the difference between Populism and Democracy on the "people" side of the equation
Democracy is a system of government, Populism is a manner in which a hopeful leader (often a candidate for leadership position in a democracy) attempts to appeal to the public. They aren't even in the same domain.
The person that responded to you employed a classic "anti-rightward" trope equating populism to vicarious elite control. I fail to see the difference between Populism and Democracy on the "people" side of the equation, rather the difference is in which elites are pulling the strings.