Agree, even though the disparity is kind of odd.
If you look at media appearances from the last 20 years:
Hawkwoman (DCAU) -Shayera, Definitely Thanagarian
Hawkman (DCAU) -minimal appearances, but Egyptian reincarnation version
Hawkman (Smallville (JSA 2parter)) - Egypt reincarnation
Hawkgirl - (Same) - dead, but assumed to be the same reincarnation version
Hawkgirl (Legends of Tomorrow) - Kendra version, Egyptian reincarnation
Hawkman (Legends)- Carter, Egyptian reincarnation
Hawkman (Black Adam) - Completely unclear which version and not really addressed; appeared to have a Thanagarian ship, but could have arguably been the reincarnation version that now includes other-planet reincarnations.
Long story short, the animated Hawkwoman seems to have resonated the most due to continuous appearances over 3+ years of the JL series.
Hawkman seems to have been reinforced mostly as the Egypt reincarnations, but usually in brief appearances.
And if your only exposure to Hawkman was in Black Adam, there really wouldn't be either version to hang your hat on, because IIRC they didn't offer up an explanation.