Technically they were both Forced into Prostitution as Children, same way it's pointed out the Ladies liked Him Young applies even more so for Kohaku since Girls were married early in those days, also explains why she was actually Hunting at the beginning of the Story, cause in terms of looks she was already considered Old by most men, Hell the whole "He said I reek of Human Males" part says how much Dirty work she did for Sumiko
Except what Kohaku was doing wasn't prostitution, it was hunting
She learned to seduce men to sleep with them absorb their energy and then kill and eat them, she is basically a succubus
And while Him only did what he did under the influence of the guy with the beard whose name I forgot, Kohaku kept sleeping with men to drain and kill them even after she abondened Sumiko so clearly ended up enjoying it
This is why I don't really like how she is being painted in a sympathetic life when she remained as a murderous man eater even without Sumiko, just think how hight her body count (in both definitions) must be