So when someone says 'I'm a communist' or 'I'm a socialist' or 'I'm a capitalist' our first instinct is to accept their frame and continue the debate along familiar lines.
It's probably impossible to get any useful insights without ignoring labels and looking at practical social dynamics. So - democracy has nothing to do with being able to vote. And state planning has nothing to do with socialism or capitalism. I think more useful questions are:
Who benefits from social policy - a small caste, or a wider citizenship? How open is government? Can anyone participate, or is policy-making limited to a select group while external input is ignored or marginalised? How much influence does open public debate have on policy? Is debate bottom-up or top-down? How much diversity of opinion is available in government? How flexible are policy positions? Is policy defined by dogma or by open-minded discussion? How fluid are caste structures? Can people move between castes easily, or is socially mobility relatively static? How flexible are local and regional politics, or are they set top-down nationally? How much force is applied to non-participants and dissenters?
How open is government? Can anyone participate, or is policy-making limited to a select group while external input is ignored or marginalised?
How much influence does open public debate have on policy? Is debate bottom-up or top-down?
How much diversity of opinion is available in government?
How flexible are policy positions? Is policy defined by dogma or by open-minded discussion?
How fluid are caste structures? Can people move between castes easily, or is socially mobility relatively static?
How flexible are local and regional politics, or are they set top-down nationally?
How much force is applied to non-participants and dissenters?
If you start from Cui bono, you can then define a democracy as a political system with a high score for openness and flexibility and a low score for exclusivity and dogma.
Political mechanisms like voting, and economic mechanisms like markets, are pretty much an irrelevance. You can have both, or neither, and still be open and flexible or exclusive and dogmatic.
So I think the two axes that define real democracy are openness vs exclusivity (class peace vs class war) and flexibility vs dogma (reality-based vs fundamentalist.)
Paradoxically a benign dictatorship could be very democratic if it has a leader who listens to popular wishes rather than trying to impose them, and isn't interested in personal aggrandisement.
It could easily be more democratic than any of our so-called Western democracies, where voting is entertaining as public theatre but real influence is reserved for lobbyists and special interest groups.
Reading your questions, what came to mind as a relatively short label for the preferred answers is "an open, flexible society", and I see that you highlight these words below. Even shorter would be "an open society". Like any short label, however, these must be given meaning by a context of discussion, and are subject to the threat of being taken and twisted. Words and ideas I offer here may be used freely and without attribution.