Populism is, by its most basic definition, “the quality of appealing to or being aimed at ordinary people/the common man” (as opposed to the “elites”). In politics that populism can be driven by leftist ideology (e.g Corbyn, Sanders) or from the right (e.g. Le Pen, Farage, Il Douche).
What confuses things a little is that right-wing populists are almost always authoritarian, and that they’re really more interested in making themselves a new elite the moment they take control (despite their rhetoric, “ordinary people” are only a means to power). Further confusing things is the fact that right-wing populists often ally with existing conservative elites (who think that the populists can be controlled) with the goal of either turning on them or forcing them to join the new elite. Another confusing element is that right-wing populist demagogues are often confidence artists who only pretend they’re not members of the elite.
Putin actually does support some radical left-wing populist movements, although not to the degree he supports the right-wing ones. For obvious reasons (since he himself is a corrupt crony capitalist plutocrat) he doesn’t support the less radical anti-plutocratic left-wing populists you mention.
