The G number is a ratio of how your projectile looks/behaves compared to a standardized shape.
The G1 shape is basically an old style canon projectile from the 1880's.
The G7 shape looks more like a modern projectile: long, boat tail, secant ogive. You generally get better results from ballistic calculators when using the G7 number.
BC is a measure of how well a particular projectile overcomes air resistance in flight. The higher the number, the better the performance of the projectile (the less it drops). If you are comparing BCs, it is important to compare like for like (G1 to G1).
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