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Kukui, Hau, and Hala are all named after important polynesian trees. That they normally brought over along with a shit ton of other plants on island colonization voyages and spread across the Pacific.
Note that Hau and Hala extremely recently have been found to have actually have made it to Hawaii on their own pre-polynesian contact due to being in the sub-fossil layer before that period. This is probably irrelevant.
Another similarity the plants share is that they are all relatively coastal and dry, but they can grow up into the mountains. Hawaiians favored the trees so they cultivated all three of them.
Kukui, also known as candle nut, was extremely important to the polynesians in that it was their primary fuel source, and it could generally sustain a flame so that it could be used as a candle. It was believed to be the physical form of the boar god, and the oily film could be used to view underwater when fishing. Other than that, it has some food and medicinal properties, but everything has those.
Hau is a hibiscus tree. It was generally a good woodworking plant. Canoes, cordage, resisted rot, practice spears, kite beams, flowers strung into leis, etc. Nothing really special.
Hala trees were also all around useful. The fruit could be used as horrible starchy food. The spined leaves were used for thatching. General medicinal and woodworking use. Seeds were strung into leis, etc.
