which is the difference and similarities between this two types of democracy? Is there any political structural differences or philosophical differences among them ? Which type of political system helps country to be more progressive and helps to increase transparency?
In Germany the term "direct democracy" generally refers to political issues being decided directly by a public vote of the people. In ancient Greece laws were actually made by all voters (male citizens) coming together in a public space to vote on public issues.
Today, virtually all democratic countries are representative democracies, meaning the people do not vote on laws themselves, but vote for representatives, who make laws and deal with political issues on behalf of the people. This can be referred to as indirect democracy, because the will of the people is implemented indirectly (via representatives).
Structurally, this lead to the people being less powerful, because they transfer a part of their power to the representatives. The representatives are not bound by the will of the people, but can decide themselves what to vote for in parliament. The people can only express their will by voting for or against a representative from time to time. This leads to a typical principal agent problem. Furthermore, in an indirect democracy the people do not have to vote on every issue. Since political issues are abundant and complex, having a purely direct democracy would require the people to spend most of their time dealing with these issues leaving little time for anything else.