"Independent" refers to party affiliation. That is, s/he doesn't have one. That's what I am. The term does NOT refer to stance on issues (progressive, liberal, moderate, conservative, totally batshit wingnut). There are various reasons for not becoming affiliated with a political party.
Some people call themselves independent, when what they mean is moderate, AND they actually belong to a political party. But that is wrong, IMO.
"Moderate" means left of center or right of center. ("Centrist" is in the middle.) You can be a moderate Democrat, a moderate Republican, a moderate Independent. I can't imagine there being a moderate Libertarian...the party itself is extreme.
I used to consider myself a moderate Independent, until the right got so wacko. It has driven me more toward the liberal side.
I believe that most people in the country are moderates, not wanting an extreme either way. This is why moderates are usually elected President, and a Kucinich or an Eric Cantor can't win the Presidency. Extreme positions scare the skivies off moderates. OR...the candidate has to pretend to be moderate to get elected. (Exception would be Romney; that's how screwed up things are these days. The Republican Party has gotten taken over by extremists, so Romney has to pretend not to be as moderate as he is.)
In a state where a person doesn't register to a political party, it's easy to consider yourself one thing or another, like here in Texas. When I lived in Louisiana, where you have to register to a party, I registered as a Democrat.
There' a lot of talk about independents in teh middle who haven't made up their minds. I think THOSE people are just called independents for lack of a better term. Stupid, uninformed, self-involved people who don't care a twit about current events describes them better. Real independents like myself have made up their minds. Most are Republicans or right of center, I've heard, so it's possible they really are undecided because they just don't want to vote for Romney, but they don't like Obama, so don't know what to do. Maybe.
I'm probably really a Democrat, I guess. I just have issues with BOTH parties...the money, the corruption, the payoffs, the lack of a third party, etc. So I don't like to affiliate myself with the party structure.