Which is more appropriate?
"Hawaii" or "Hawaiʻi": is the difference very significant? And which is more appropriate to use over the other? Are there situations in which one would be better to use than the other?
Also, is there a reason why itʻs "Hawaiian" and not "Hawaiʻian"?
Aloha mai e @BlockedBlock, e kala mai, is your question about pronunciation or about how it is written?
Koʻu manaʻo on this is that for written standards, it should always be "Hawaiʻi" when possible (keyboard availability; capability to print this on signage, etc). Same with any word with a kahakō (macron), as in Lānaʻi. This does 2 things, it encourages proper pronunciation in an era where there are less fluent Hawaiian speakers (or more learners of Hawaiian). The second thing it does is honors those kūpuna who in the Hawaiian Renaissance, went through the effort to standardize written Hawaiian to include the ʻokina (ʻ) and kahakō so that the Hawaiian language would live on (knowing very well that future generations may not have the resources of native speakers facilitating correct pronunciation) (see Queen Salote of Tonga, Mary Kawena Pukuʻi and others).
For "Hawaiian" vs. "Hawaiʻian" remember that is this an ENGLISH WORD, not he huaʻōlelo hawaiʻi, so the correct English spelling for this is without the ʻokina (ʻ) as the English word does not have this pronounced. For those who wish to express it as "Hawaiʻian;" however, I also support this but for different reasons. This emphasizes indigenous Hawaiian people as existing in an English-phrased. By reclaiming our diacritical marks, and using them in written, we are able to decolonize our minds step by step. Some people may feel this is Pono for them, and should be accepted. One day it is the usage of "hawaiʻian language" or "hawaiʻian people" and the next it may just progress to "ʻŌlelo Hawaiʻi" and "poʻe Hawaiʻi." We can hope ^_^v.
wishing that this is helpful for you!