The reason why you will find number 7 1/2, 8, and 9 loads is because these are the shot sizes used for shooting Clays. Fact is that almost any shotgun range will have postings that state that only # 7 1/2, 8, and 9 may be used.

Number 7 1/2 loads are typically used for shooting Trap, because Trap features targets thrown at a greater distance from the shooters position. However some Sporting Clays shooters will keep some # 7 1/2 shot shells in their pocket for the stands that feature long range targets. BTW, Sporting Clays can have shooting distances ranging from 10 yards out to 60 yards.

Number 8 loads are basically All Rounders and probably the most common shot size for shooting Sporting Clays because they will work well at any distance out to about 50 yards. As an general purpose shot size it will also be seen in Skeet, 5 Stand, and Trap.

Number 9 loads are the Standard for shooting Skeet. However # 8 or 7 1/2 will also work well in 20 and 12 gauge loads. Once you get down to 28 and 410 #9 produces shot clouds with smaller "holes" so it's distinctly preferred for these calibers.