These are important terms to understand.
This is the academic definition of our current system of Government.
Voters elect representatives. Those representatives elect a Government. There is no direct contact between the Government and the voter. The Government is only required to communicate with and seek the approval of the person voters have elected as their representative.
“Democracy” is what we inaccurately call our current system of Government.
What democracy actually is is direct participation on the part of the voter in decision making. Democracy is not elections. Elections are a system of representative government.
Direct Democracy is a system in which referendums are held to allow the wider population overrule the decisions of representatives, or to propose new laws.
Direct democracy suffers from the same flaws as Representative Government, in that it still allows the Oligarchy (see below) to control outcomes, as Direct Democracy is still based on voting.
That said, a system based on Sortition can contain elements of Direct Democracy. For instance, if a particular decision could not be made by the parliament, it could be referred to a referendum.
This is the most important one.
Oligrachy is a system of power (ie Government) in which power effectively rests with a small number of people.
This is the most accurate description of our current system of Government. The “oligarchs” are the people who own and control the media, the people who fund political parties, and the political parties themselves (including non-registered political organisations who organise around “independent” politicians).
Oligarchy is not a conspiracy theory. It has not been foisted on us by evil or malicious forces. It is something we have allowed to develop through complacency.
And the final and key point is this:
Representative Government, or more precisely, any system based on elections, will always lead to Oligarchy. The only way to establish true democracy is to remove the system that allows Oligarchy to develop. The only way to remove the current system is to replace elections with Sortition.