The direct democracy or pure democracy it´s a form of democracy in which the people directly decides on policy initiatives, it differs from the representative democracy; the one that it´s currently established in the majority of the countries; because in that the people choose the representantives and they are those who decide the policies to carry on. In the representative democracy the people do not govern, it´s a common mistake to mix both concepts.
Two different forms of direct democracy are participatory democracy and deliberative democracy. The deliberative democracy is a form in which the deliberation it´s a central matter to the decisions and it is seen as an amalgalm of the direct and the representative democracies. It holds that for a democratic decision to be legitimate, it must be preceded by an authentic deliberation not a mere voting.
The participatory democracy is one that emphasizes the broad participation of everybody but it demands to the citizens to be more involved in the political participation.
I think that a group taking a vote on something is an example of a participatory democracy because everyone have the same power to create consensus and, at last it would win the iniciative that obtain more votes. If the example was a representative democracy then the group would have to vote for only one person to make a decision and then the group will follow the "leader" choice althought it goes against the majority of what the group wants.
I hope the answer to be useful for you. Regards.
