Their names pretty much explain it all. Specific rate springs are designed to compress at the same rate, say 450 lbs/in. In otherwords, to compress that spring 1 inch, it would take 450 lbs of pressure. To compress it 2 inches, it would take 900 lbs of pressure, and so on.
Progressive, also known as variable rate springs are designed to compress at a range of pressures. Typically, you will see the specs as a range, such as 900-1050 lbs/in. For example, it may take 900lbs to compress the spring the first inch, maybe an additional 975lbs to compress the second inch, and an additional 1050lbs to compress the third.
Most street driven vehicles come with progressive/variable rate springs. While you are driving at low speed, perhaps over small bumps in the road, these springs offer a comfortable ride. When you want to thrash it around at high speed, it takes progressively more pressure to make them compress. So, they often offer good handling characteristics. Assuming the shocks, struts, and springs are matched well with the weight distribution and suspension geometry of the vehicle.
Specific rate springs are more of a thing for hardcore/professional race teams that change springs frequently from track to track. Yes, you can purchase and use them on your street or race vehicle, but you had better know exactly what you are doing.
At any rate, I would consult with a professional regarding the proper selection of suspension components. Anyone will sell you parts, but as expensive as they can be, why take chances? I'd suggest talking with the folks at Maximum Motorsports, Griggs Racing, Steeda, Kenny Brown, etc. In fact, spend the few bucks of long distance charges and talk with them all. Your car is not my car, or your friend's car, and so on. Just because a particular spring-shock-strut combo works for another car, doesn't mean the same will work well with your car.