I hear they make good pets due to their size and are easier to tame, but that’s about it.Bobwhite take quite a bit longer. They take about 2 1/2 months to mature and then another month before starting to lay eggs.
They are definitely two different unrelated animals. Coturnix are in the same family as pheasant but Bobwhite, like other new world like California and Mountain quail are in their own family. The several dozen species in this family are permanent residents throughout their range.
Coturnix can live in a cage but IMO Bobwhite need more room. One advantage of Bobwhite is that they will brood their own eggs/chicks. That's a benefit for homesteaders living off the grid.
I just remember hearing their unmistakable call almost daily when living on the farm.
ETA
Can someone explain what the attraction is to raising buttonquail?