it's a deliberate reframing
The idea is to avoid the positive connotations of "democratic", and reduce it to a label that just means a collection of Democrats.
Or as Republicans pronounce it, "Democrats! [hawk ptooey!]". The sound is just a little bit harsher, too, and lends itself to digging in and turning it into a sneer. Republicans don't want to be seen sneering at the concept of "democratic", so they had to rename the Democratic Party in order to get in their full quota of sneering at Democrats.