Different Elasian. Elaan was the Dolhman of Elas ("Elasian"). Melora was an "Elaysian" from a different planet entirely (the writers probably should have realized how similar the names were but apparently forgot about the name in the classic TOS episode or just didn't care).
Good episode. But yeah, Melora and Elaan of Troyius are from two entirely different planets and humanoid species that just happen to have uncomfortably similar names. Hope that helps a little.