Democracy isn’t an economic system.

Yes true.

Communism is both non democratic, and an economic system. You cannot have democracy and communism at the same time.

Socialism is in the same vein, but today we often conflate it with social democracy (which seems to be the best of the two worlds nowadays IMO).

Communism is not democratic. Read up ffs. It’s not democratic.

Whilst Communism itself (i.e. the utopia were everybody has the same - i.e. Equality Of Outcomes - which, by the way, has never been achieved anywhere in the world) isn’t anti-democratic per-se, the only ideologies that aim to reach it, such as Marxism and all its derivatives, have it being done via the Dictatorship Of The Proletariat (hence the revolutions and then takeover of power in all the self-proclaimed “Communist” countries), which is most definitelly anti-Democratic.

However Leftwing principles aren’t incompatible with Democracy, so Leftwing ideologies exist - such as Social Democracy - which strive for “the greater good for the greatest number” without the need for autoritarian means (i.e. using things like Universal Healthcare, Universal Education, Progressive Taxation and other such things within the context of Democracy, to make the society more equal, especially in terms of Equality Of Opportunities). None of these expects to ever achieve Communist - they actually accept that it’s impossible given human nature - but still try and make a more equal society which maximizes the quality of life for all people.

This stuff has definitelly been done in practice in Democratic nations (for example those in Scandinavia) overlayed on some amount of Capitalism, though as of late with Neoliberalism (which is definitelly incompatible with it) things have been going backwards even there.

I think it’s quite oversimplifying it to say that any ideology that aims for a more equal world is “communism” as that one is quite a specific outcome which can’t really be achieved without forcing people to do certain things against their will and, as history has shown everytime that’s tried, the outcome of taking over power to try and reach Communism is never Communism but rather a new Elite who keep themselves in power through repressing, claim to be representatives of the Proletariat (which giving themselves all kinds of priviledges the proletariat never has) and use certain slogans to try and pass themselves as leftwing.

Judging by the Communist Party in my own country - with it’s habits of Party First in everything (even above those they claim to defend), always having things approved by unanimity in their conventions and hard-on for autocrats - I very much doubt we will ever see anybody coming from that background capable of taking their country in a more equal direction within the constraints of Democracy: they’re simply far too autoritarian, mindless slogan parroting and tribalist to be capable to, in a democratic society, create the necessary consensus for the steady and stable moving of a country towards a grand objective.