Well, you have several questions here. First of all, the BMI is a set calculation - it makes no sense that you'd get a 31 from Curves and a 25.4 with some other calculator. There is a set formula involved. At 156 lbs, someone who is 5' 3.75" has a BMI of 27, in the middle of the "overweight" range. The formula stays the same, so your number won't change unless your height or weight changes.
As for whether BMI is a good indicator of body fat, it depends. It has known inaccuracies for certain groups (Very muscular groups like athletes, or very non-muscular groups like the elderly, for example). Because it doesn't take into account your age, sex, frame size, etc, it can only provide you with an AVERAGE value for all people with the same height and weight as you.
It sounds like, though, you didn't get measured for BMI at Curves - you got measured for actual body fat percentage, with a bioelectrical impedence device. The accuracy of these devices depends on a good number of things (the device itself may be a less accurate or more accurate one, etc). There are more accurate ways to measure body fat percentage, like hydrostatic weighing, but they are more expensive and harder to find.
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