When your done with this, explain to me why 1 7/8 and 2 in balls coexist.
Smaller balls equal lower cost and way back when, when most people drove cars and hung balls off their rear chrome bumper on the station wagon to tow a small boat or pop up camper, the 2000# limit was enough.
As trucks became more capable and as the Ford F series started to become the most popular selling model for 40+ years, people transitioned from thin gauge bumper tows with bolted on plates and a 1 7/8" ball, to step and tow bumpers capable of 3500# on a good day attached to trucks. This required a 2" ball with a larger shank and bigger surface area. As people twisted step and tow bumpers off their vehicles, solutions were needed.
Then as trucks became more powerful and with heavier frames, receiver hitches were installed, that upped that 2" ball to 5k and then 7k loads. Once the limits of that shank and surface area were reached, they transitioned to the 10k 2 5/16 ball which matches the limit of the size trailer you can tow without having a CDL.
Except in cases of an RV camper/5th wheel where a 2 5/16 is good for up to 21k, with the limit being under 24,999 before needing that CDL.
1 7/8 and 2" balls do not really coexist, you would be hard pressed to find any major OEM that sells a trailer that has a 1 7/8" coupler on it. Maybe on a folding trailer with 4 lug wheels with a 1500# GVWR. But, most people go with bigger is better and the standard is pretty much a 2" ball with a 3000# or 3500# five lug axle.
About the only thing you will find a 1 7/8 coupler on is a trailer used to trailer a jon boat or jet ski.