It took me a bit to see where you were going, but once I did I had to agree. (For the benefit of anyone who isn't a history buff) when populism first became a political force in the U.S. (the late 1820's)--as a reaction to the elitism of the Planter class (and led, of course, by a Planter, in the form of Andrew Jackson)--the movement was called "the Democracy."

One point that has to be made is that in presidential elections in the U.S. the popular vote doesn't decide who wins--only one Republican candidate has received a majority of the vote since 1988 (the younger Bush in 2004--so two won without it in that span of time: Bush in 2000 and Trump in 2016).

I do think your definitions of "liberal" and "democrat" are accurate as far as they go, but, frankly, they seem to me to be designed to make it look as though "liberal" (which uncareful people on both sides of the political divide will read as 'the political "left"'--and read no further) is inherently anti-democratic.