If you open a margin account, does this mean that you are putting your OWN money in the margin account which is supervised by a broker and to whom you pay interest to?
A margin account is one where you can borrow money from your broker to buy securities. The loan is collateralized by your cash and/or marginable securities. You pay interest to the broker on cash borrowed. However, you do not have to borrow cash from your broker.
Some strategies cannot be done in a cash account and require a margin account: shorting securities, selling uncovered options...
A managed account is one that is supervised by a broker, to whom you a fee. The fee tends to be an annual percentage of the value of your account.