Well if you look at Syria and Egypt they were long run by "presidents" that were, and still in the case of Syria long-time dictators. Just because you have a title or a name does not make it what it actually is. In order to win the revolution in China the Communists wanted to make the people think they were on their side. They are not going to call themselves dictators, or reveal that they wanted to set up a government that gave people at the top wealth and rights, while depriving the masses. No one would go along with that, so of course governments are going to come up with more savvy names for what they are. Just like company that is not so good at selling things is going to do everything they can to improve their image.
Another thing I find misleading is why some Americans want to insist that America is only a republic, but discount our strong democratic tradition as a republic. In the classic sense a republic is a representative government where only a small number of people are allowed to vote, such as in the days of the Greek republic, and the early days of the United States when only white men were allowed to vote. Thus, have a democratic emphasis on a Republic is crucial, and I would prefer to see more people educated about how our government works and eventually become more of a representative and direct democracy.
That is the way things are going with our propositions here in California where anyone who can get a petition with enough votes can get something on the ballot. By the way there are drawbacks to our republican form of government at the moment, such as the amount of power our Supreme Court has. I believe we need a Supreme Court, but we also need a new Constitutional Convention that might realign how much power, and how long people serve on it. I would also like to see the end of the electoral college, and many other things that were created at the inception of our country when the founding fathers were frightened of majority rule. The reality is just because a small group of people is making decisions does not mean these are always better, and sometimes when a popular decision is made, we as voters and citizens have to learn to agree to disagree.