Hedge funds are different to both mutual and index funds. I'll explain why in a sec. First there are two terms you need to understand, alpha and beta.
Beta is matching the market. If you invest in an index fund you will get the beta return less fees. If you invest in an ETF (Exchange Traded Fund) then you'll make the beta return less commissions. Passive investors should always look to get the beta return by investing in index funds or ETFs. Beta investing is positive sum, the market has risen historically.
Alpha is beating the market or underperforming the market. This is what active investors try to achieve. Alpha investing is a zero sum game, when one person beats the market another person underperforms by the same amount.
Index funds/ETFs are long only and get beta return only. They do not attempt to get alpha return.
Mutual funds are long only so they get the beta return and attempt to get alpha returns as well. Once fees are taken into account the majority fail to get a positive alpha return for their clients, and hence underperform the market.
Hedge funds on the other hand, are 50% long and 50% short, hence the term hedge in the name. They get zero beta return. They attempt to achieve alpha returns and, because they have the best managers, usually do. Hedge funds are far less volatile then mutual funds/index funds/ETFs because they suffer much, much less of the volatility of the market (which is approx 17-18% standard deviation I think).
Hedge funds are a low risk asset. If you leveraged Hedge funds to the same risk as the market then Hedge funds have consistently outperformed the market historically. Or, in other words, Hedge funds outperform the market on a risk adjusted basis. However, Hedge funds shouldn't really be compared to standard market benchmarks, such as the SP-500, in this way because they are very different investment vehicles.
Hedge funds are less regulated then mutual funds, this means they have far more choice over what companies to invest in and can move money around easier, even taking it out of the market if it suits them. This also means that they are a lot less transparent then mutual funds and there have been some notable blow ups. Hedge funds (at least the best ones) have very high minimum investments (low millions) and often do not allow you to withdraw your funds for a certain length of time.
Links for more info on hedge funds:
http://www.hedgeworld.com/
http://www.vanhedge.com/