In the past, like over 50 years ago, each spring was vibrated to its balance. Each balance, while superficially identical, could be different enough from the next one in the box to make the hairsprings incompatible. The modern method is more automatic, the springs are colleted then cut to a given length, the terminal curve formed, stud attached. They are then each tested and graded into about 20 categories; the balances are likewise graded into 20 categories. If you look at the results of the categorization, it makes a nice bell curve, with the majority falling within perhaps 4-5 middle spots, the rest dispersed in decreasing numbers towards the ends.
The balances and hairspring are just mated according to the category. If you try to mate a Cat 1 spring to a Cat 20 balance it won't work at all. If you try between Cat 9,10,11, it may work OK. Of course there's no way to know which one is which once it leaves the timing department of the factory.
Balances with screws add a dimension of adaptability as you can add and remove weight easily. Solid balances can only have weight removed, and the adjustment is permanent.