Akua is a generalized term—it doesn't just refer to the Christian god. It can refer to a variety of spirits and deities. I don't know all these words with confidence, but kupuna are our ancestors, aumakua are specific protective ancestral spirits (some of whom can take animal forms), and kupua are heroic figures from stories (Maui is a good example here). I want to say kini o ke akua are multitudes of spirits and deities, or possibly different facets of a particular deities, but I might be wrong—I wasn't raised in the culture.
I guess it could be either God/dess or deity, but I've read that specifying a Goddess would be "akua wahine" (god-woman), as in "akua wahine Pele" ("Goddess Pele", who is the volcano deity who created Hawaii).
According to Wikiditionary, akua can also mean "spirit" or "ghost", although it's probably most common to translate the word to "God" because how it's used religiously.
He aha ka huaʻōlelo no God? = What is the word for Akua?
New Hawaiian Dictionary
God, goddess, spirit, ghost, devil, image, idol, corpse; divine, supernatural, godly. Akua might mate with humans and give birth to normal humans, moʻo, or kupua (Nānā 23). Children of Kamehameha by Keopuolani were sometimes referred to as akua because of their high rank. Kauā, or outcasts, were sometimes called akua because they were despised as ghosts.