Due to the merging of Earth 1 & Earth 2 in the aftermath of Crisis on Earths, Hawkman arguably takes the crown jewel of comicdom's most convoluted characters.
Robert Vendetti's explaination of simultaneous reincarnations is probably the best solution to the character's contradictory history we will ever get, but this doesn't explain why Ancient Egypt and Thanagar both produced Hawk-inspired heroes with virtually the same costumes and usage of Nth/Ninth Metal.
Also to make matters more confusing, in JLA Incarnations #1, it is retconned that the Hawkman and Hawkgirl of the Justice Society of America were the same Hawkman and Hawkgirl of the Justice League of America. If you sit down and think about this for one second, this makes absolutely no sense: the Golden Age Hawks were reincarnated Egyptian royalty while the Silver Age Hawks were extraterrestrial police officers.
The most concise solutions to me are that:
A. Carter and Shiera Hall perished after the dissolution of the JSA and before the formation of the JLA. Kator and Shayera Hol were reincarnations of the originals.
B. The Golden and Silver Age Hawks are completely seperate characters, no reincarnation involved.
The similarities between the two different Hawkmen and Hawkgirls can be boiled down to the an offshoot of the Feitherians(who Infinity Inc readers will be familiar with) migrating to another planet and bring Nth Metal along with them. Over the centuries, these Feitherians evolve into looking more humanoid in appearance, similar to how the Klongons suddenly developed head ridges in Star Trek the Next Generation. Kator and Sheyara are named in homage to their Golden Age counterparts.
As for the Kator and Sheyara introduced in Hawkworld? The same logic applied to them. Either they are reincarnations of the Silver Age Hawks or completely seperate characters. For this to work, the original Shayera and Kator would have to die in between the end of the 1986 Hawkman series and the 1990 Hawkworld miniseries.