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No, they are not the same.

Mutual funds that track an index or use a combination of indexes (may include bond or gold or other indexes than stocks) in the fund are NOT considered "managed funds" because what is in the fund is already set by the index. Those funds have lower fees because they don't need the same level of management to pick, or buy and sell individual stocks.

The term is usually used to distinguish between index funds and other funds.

Mutual funds are more likely to be passively managed with lower expenses. A managed fund is more likely to have higher portfolio turnover and higher expenses.

A mutual fund can only exist in a "managed" environment; but there are managed funds that are not mutual, so the terms are usually synonymous, but not always.

It's pretty much the same thing. The manager gets a percentage every year of what you have invested from the money that he gambles wheter or not he gains or loses. Why pay someone to gamble for you unless they can beat the market.

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