1) The two terms are interchangable depending on moral alignment
2) Possible translation issues could screw up everything in an anime. Lest we all forget the horrible tragedy of Digimon season two.
What happened in Digimon O.o
As for Bleach, the actual Kanji came up for it. The character said "Boku wa Shinigami desu" and then the translation came up for it.
Even Naruto had the actual God of Death Demon thingy be summoned, and they called it the Shinigami.
Tsukiyomi is also a move in Naruto, where the person is sent into the God of the Moons world.
Or 3) They might just have used the term without it being the same thing as in real life. Harle/Tsukiyomi sure doesn't look male to me.
Yes, but everything that is related to the moon is related with Harle (Tsukiyomi). And we all know saw a part of her relation to the Dark Moon, and we all know that Japanese games love to have puns in them. It'd be the basic principal of Tsukiyomi being related to the moon, and since she is a God in her own right, one being of that moon, then she is indeed literally Tsukiyomi, no matter what her gender may be.