Almost every government now calls itself a democracy.

A Direct Democracy typically results in anarchy. I am not aware of any.

Communist East Germany (The German Democratic Republic) called itself a Democracy. It built a wall to keep it's citizens from fleeing to escape its definition.

The Soviet Union was by one definition, a Republic (a government without a monarch) but it was anything but a “Representative Democratic” Republic. It really didn't give power to the people. It's one party, the Communist Party, chose the Politburo, not the people. The USSR violated natural law: there was no incentive for either the over-taxed, productive Peters or the subsidized, non-productive Pauls and the result was a non-productive, mediocre society. That definition of Democracy went broke.

Venezuela calls itself a Democracy. It's a far cry from what American's consider a Democracy. At one point, there were several political parties in Venezuela. After the “Democratic Revolution” Hugo Chavez and his supporters (somehow) secured all 167 seats in the National Assembly. Then, Chavez's National Assembly voted to merge all factions into Chavez's United Socialist Party. I believe that there is now just one party with Chavez as its “Democratic” leader. Even though they hold fake elections, Venezuela is by definition an Oligarchy, Chavez and buddies.

All European countries are now considered to varying degrees, Social Democracies. The people of those countries still have a voice but they vote increasingly to give more of their personal responsibilty to the state. None of them are exactly Marxist because they not revolutionary. They are civilly allowing social and economic equality to evolve over time. They will likely realign (again and again) and become totalitarian regimes like Venezuela.

The US is a Democratic Representative Republic but the people are obese and content. We are allowing government to take over increasing levels of our care and feeding. Government continues to force social and economic justice. Like all other societies that have taken that route, I suspect the US will become increasingly poorer and weaker and a wealthier and more powerful country will simply consume us.

In the future, the only definition of Democracy that will matter for us is the one that is written in Mandarin.

Furthermore, representative democracy and republicanism are practically inseparable, though not indistinguishable, concepts, and the partisan politics of party nomenclature is the only reason to get so upset about the choice of terms. Direct democracy is the real distinct alternative to republicanism, and it has primarily been a tool of the right wing; to link it to socialist ideology is just silly.