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A fixed rate is simply that, a rate that is fixed at a certain percentage. Your card may have a fixed rate of 15.99%, when the CARD act goes into effect, credit card companies cannot change this without giving you a 45 day notice, at which during that time and up to 2 billing cycles later, you can cancel your card and pay off your balance at the fixed rate you had before the notice was mailed out.
A variable rate is tied to the prime rate and moves up or down as the prime rate moves, this gives credit card companies an opportunity to get more interest charges, as the prime rate is expected to rise.