Iran is a theocratic autocracy. Only the autocrat and his supporters bear any significant responsibility for the actions of the government there.
The key distinguishing factor being that in a democracy powers are derived from the consent of the governed, as opposed to other forms of government (including some "constitutional republics") which do not allow open democratic elections.
Democratic Republic, just like People's Republic, is actually a euphemism for communism.
What you are describing is "representative government" and "self government" not necessarily democracy. The will of the people is an abstract concept that is, depending on the issue, not always accurately measurable by equally weighted vote of a subset of the people that are enfranchised.