The Cliff note answer is that the difference applies to the aerodynamic shape difference between bullets. Generally, a more traditional flat base spitzer shaped bullet would use the G1 formula. The streamlined, pointed, boar tail, VLD style bullets would use the G7 formula. This difference is expressed by the bullts ballistic cooefficient. When using a ballistic calculator the different algorithms used between G1 and G7 takes into account the difference in bullet shape and it's effect on retaining velocity, which increases in importance as the range increases. The result will be more accurate sight corrections for elevation and windage. Hope this helps.
The G1 BC numbers are based on a bullet model that Was used years ago and it is a standard Ogive
with a flat base. The modern bullet makers like to use the G1 because it drives the BC of there "Better" shaped bullet to higher numbers.
The G7 Model is modern and more closely matches the profile of the modern bullets. Even though the BC numbers go down when used, the results are more accurate.
So when you see a BC in the 7s or 8s it is based on the G1 system.
Bryan Litz has lots of information on the subject that is worth the read.
My simple explanation of G1 vs. G7 is similar to what you've read above. The practical effect you'll see is that when you look at a bullets G1 BC, it varies a great deal over the range of flight speed from muzzle to the target. The G7 BC has much less variation. As a result, you'll see more error in trajectory predictions using the G1 model for modern bullets.
It's also harder to nail down what the G1 BC actually is due to the velocity variation. If you say a bullet has a G1 BC of .500, I have to ask: "at what speed?" If you say a bullet has a G7 BC of .245, I can rest assured this will hold true for the practical range of bullet flight speeds.