This is not hard to comprehend for those who actually care about the knowledge they wish to display.
“Democratic” is an adjective that is defined as pertaining to or of the nature of democracy or a democracy or advocating or upholding democracy. It does NOT, in any way, refer to the political party.
“Democrat” is both a noun and adjective that names the political party and describes aspects of politics that are made, managed, or connected to said party.
Thus, we may have democratic elections as defined by the Constitution, but votes are for Democrat, Republican, Independent, third-party candidates, NOT “Democratic”, Republican, etc. candidates.
It is important that we express the difference.