I checked over a dozen of 7/16” studs in the system and they all use 5/8” sockets.9/16" also but 9/16" is kind of considered a "specialty" or "automotive" size and sometimes only at true fastener houses -- although I've seen it in Hillman stuff at my Ace Hardware. Many smaller "hardware" stores jump 1/2" to 5/8"
I’m guessing the “other” sizes are the antique light medium heavy fine/coarse “nut” crap used in AG? I would have to check but probably deprecated from SAE (50’s)
or listed as an alternative size for square hardware.
(Nothing like USS not equaling SAE)
So What application?
Now very very old (obsolete) 1/4” hardware comes with an alternate size head, (system has prints from 1952) but that other size is deprecated from SAE standards, though square head bolts still exist in some sizes which drives some weirdness for wrench/socket sizes.